Papers

A recent manuscript of OpenAI asserts that Landau-Siegel zeros do not exist. Here, we give a detailed account of its argument, arranged as a direct proof with explicit constants. There are absolute constants $q_0$ and $\delta_0>0$ such that, for every primitive real Dirichlet character $\chi$ of conductor $q\ge q_0$, every real zero $\beta\in(0,1)$ of $L(s,\chi)$ satisfies $(1-\beta)\log q\ge\delta_0$, and one can take $q_0=10^{10}$ and $\delta_0=3.0\times 10^{-3}$. Combined with a recent computation of Lu, Zaman, and Zhao, this result yields the bound $(1-\beta)\log q\ge 3.0\times 10^{-3}$ for every conductor $q\ge 3$. The proof is an interpolation determinant argument in the biquadratic field generated by $\sqrt{2}$ over the quadratic field attached to $\chi$. A real zero close to one forces $\chi(p)=-1$ for most primes $p$, and the Frobenius congruence at these primes makes a certain nonzero determinant divisible by higher powers of these primes than its Archimedean size allows. The underlying ideas are those of the OpenAI manuscript. The explicit constants, and the presentation, are new.

Large Language Models accelerate software development but introduce severe security vulnerabilities. This systematic review investigates security risks in automated coding, benchmark limitations, and the role of human developers. Findings indicate that models frequently generate insecure code and faulty patches due to training data biases. Additionally, the models themselves are susceptible to direct attacks. Current evaluation methods suffer from data contamination and lack robust security metrics. Consequently, human oversight remains essential. Safer integration of automation will require more security-aware model architectures, stronger security-specific benchmarks, and more effective human-AI collaboration frameworks to mitigate these systemic risks.

Independently authored skills can impose incompatible requirements, competing preferences, and redundant instructions when jointly loaded by an LLM agent. We propose SkillFusion, an offline compiler that reconciles these interactions into a reusable merged skill. Its central idea is to make composition decisions explicit through typed, scoped constraints linked to their source directives. A type-scope gate selects candidate interactions, while selective fallback revisits pairs potentially missed by structural pruning. A classifier identifies interaction types, and an adversarial verifier re-examines uncertain judgments. The resolver applies conditional routing or explicit priorities to hard conflicts, verified abstraction to soft conflicts, and deduplication to redundant instructions. Source-linked checks guide synthesis and compression, and metadata synthesis supports discovery of the merged skill. The resulting artifact retains associated scripts and resources and can be reused across tasks and executor models. SkillFusion achieves the highest mean Success among evaluated non-oracle methods on all three agent benchmarks and on both transfer benchmarks across three executor models. At the largest tested instruction configurations, it achieves over 2.5 times the Success of unresolved multi-skill loading, highlighting the growing value of reconciliation as composition becomes more demanding. The code will be open-sourced after the review process concludes.

We study games on finite graphs with labelled or weighted edges in which plays end as soon as the first loop is formed. The resulting play has a lasso shape: a path (head) followed by a cycle (loop). We consider two semantics for determining the winner: the loop semantics, where only the loop matters, and the lasso semantics, where the entire play is taken into account. We show that adopting the lasso semantics may have a dramatic impact on both the complexity of the game and the memory required to play optimally. Mean-payoff games with lasso semantics are no longer positionally determined, and the threshold problem – deciding whether the value of the game is at least 0 – is PSPACE-complete. In contrast, lasso parity games are equivalent to weak parity games, remain positionally determined and are solvable in polynomial time. Furthermore, we show that if a positionally determined winning objective is closed under cyclic permutation and both the objective and its complement are closed under concatenation, then it is equivalent to the parity objective. Finally, we consider mod-k games, where the winner depends on the length of the path modulo k >= 2. We show that these games, in both semantics, are PSPACE-complete. Alongside computational complexity, we analyze the memory required to play optimally. We establish that for any game positionally determined in loop semantics, memory of size 2^n is sufficient in lasso semantics. We complement this by showing exponential memory lower bounds for lasso mean-payoff and mod-k games.

We present asymptotically optimal translations from linear temporal logic with past to limit-deterministic Buchi automata and onwards to deterministic parity automata. In contrast to previously known translations involving past, the ones presented here are incremental: states and transitions can be constructed as needed on-the-fly, and they do not involve backtracking in order to correct for temporal inconsistencies. The past is naturally encoded in the formula by alternating between weak and strong versions of past operators. To handle the difficulties that arise from the alternation of least and greatest fix-point operators (such as between the "until" operator and its weak counterpart), we rewrite the given formula based on the infinitary behavior of a given word with respect to subformulae rooted with such operators.

Timing information leakage occurs whenever an attacker successfully deduces confidential internal information by observing some timed information such as the total duration of a run. Timed automata (TAs) are an extension of finite-state automata with a set of clocks evolving at the same rate and that can be tested or reset. Hence, this formalism is able to represent systems involving timing constraints reacting to the passage of time. Some of the transitions in a timed automaton may be controlled, i.e., enabled or disabled, to limit the runs that are allowed. Execution-time opacity (ET-opacity) aims at studying timing information leakage through the analysis of timed automata. More precisely, the ET-opacity problem consists in deciding whether an attacker can deduce whether some secret locations were visited by a run, solely from the run's duration. When control is allowed, the goal becomes to find a strategy that blocks the runs leaking information. This problem has been shown decidable for TAs, with and without control. However, these existing results only provide upper bounds on the complexity of the ET-opacity problem, sometimes largely above the tight bound. Our main contribution is to provide tight lower bounds for those two results. Moreover, for controllable TAs, two variants of ET-opacity (depending on whether detecting if a run did not visit a secret location represents an information leakage or not, and named full and weak ET-opacity respectively) had been separately studied; we prove here that these two notions are inter-reducible.

We derive polynomial bubble duality in barycentric coordinates and construct explicit nodal bases for the first family of finite element differential forms. Logarithmic coordinates give an elementary proof of the Whitney–bubble decomposition. The Hessian of negative entropy defines a metric whose normalized Hodge star maps bubble generators to complementary-degree polynomial forms. This gives a direct geometric description of the known dualities and proves nondegeneracy of their integral pairings. Combining Whitney forms with shifted Lagrange polynomials then gives bases dual to tangential point evaluations in every dimension and order. The construction extends to scalar nodes that are unisolvent on every face. The interpolant is independent of the roots and commutes with face restriction.

One of the most well-known connections between logic and games is Pauly's representation theorem: the induced powers of individuals and coalitions in concurrent game frames correspond, in a precise sense, to a certain class of neighborhood frames. The precise sense here is what is called alpha effectivity (or alpha power): the power of a coalition is characterized by the sets of states in which it can ensure that the outcome lies by taking some joint action. This definition is inherently monotonic, and, as pointed out by van Benthem, Bezhanishvili, and Enqvist (2019), that fact can obscure relevant information about the power structure in the game: we do not know whether two sets that a coalition has the power to enforce correspond to the same joint action or to different joint actions. An alternative is to characterize the power of a coalition by its actual power (called basic power by van Benthem, Bezhanishvili, and Enqvist (2019)): the collection of sets of states, each of which corresponds to one joint action by the coalition and all possible joint actions by the other agents. It has recently been argued by Li and Ju (2025, 2026) that standard concurrent game frames rely on three assumptions that may, in some cases, be too strong: seriality, independence of agents, and determinism. This yields a total of eight different classes of general concurrent game frames. In this paper, assuming two agents, we prove that, in terms of actual powers, the eight classes of general concurrent game frames are represented by eight corresponding classes of neighborhood frames. This generalizes a result by van Benthem, Bezhanishvili, and Enqvist (2019).

Otto's Theorem characterises the bisimulation-invariant PTIME queries over graphs as exactly those that can be formulated in the polyadic mu-calculus. This extends to a characterisation of the full bisimulation-invariant exponential-time hierarchy, using a higher-order extension of the polyadic mu-calculus, called PHFL, which is naturally stratified by type order. The bisimulation-invariant fragment of k-EXPTIME is captured by the fragment of PHFL whose formulas have type order at most k. This is obtained using a generalisation of the Immerman-Vardi Theorem by Freire and Martins. Here we provide such a characterisation of the exponential-space hierarchy. We show that the bisimulation-invariant fragment of k-EXPSPACE is captured by the fragment of PHFL of type order k+1 whose formulas are tail-recursive. Tail recursion limits the interplay between fixpoints and higher-order functions so that model checking based on fixpoint iteration can be made more space efficient in a way comparable to tail recursion in programming languages. The capturing result makes use of a generalisation of Vardi's characterisation of PSPACE as first-order logic with partial fixpoints, namely that k-EXPSPACE is captured by higher-order logic of order k+1 with partial fixpoints.

We introduce Non-musical Audio to Symbolic Music Transformation (NASMT), a novel task that converts non-musical audio into symbolic music representations. Unlike automatic music transcription, which assumes musical input and a unique correct score, NASMT is inherently one-to-many and requires evaluation along two axes: input correspondence and musicality. We present Sori, an encoder–decoder Transformer that addresses this task through domain adversarial training (DAT), which bridges the gap between musical and non-musical audio in the encoder's feature space, and classifier-free guidance (CFG) with a continuous parameter~$\gamma$ that controls the trade-off between correspondence and musicality at inference time. Across objective metrics and a listening study, Sori provides effective continuous control via $\gamma$ and compares favorably with instrument-agnostic transcription models. Sori supports real-time streaming on a consumer CPU. Audio examples are available at https://soridemo0320.github.io/sori-demo/.

We prove that a Hopf algebra over an arbitrary field has a bijective antipode if either its left or right regular module has finite uniform dimension. In particular, this solves Skryabin's conjecture, posed in 2006, that every noetherian Hopf algebra has a bijective antipode. Starting from Skryabin's injectivity theorem for weakly finite Hopf algebras, we associate to each finite-dimensional subcoalgebra an essential left ideal of common denominators that is also a right coideal in the antipode image. An annihilator identity makes this image essential in the original algebra as a left module over the image, yielding finite left uniform dimension from finite right uniform dimension. A second denominator construction inside the antipode image, together with a restricted inverse-antipode identity, proves surjectivity.

In this paper, we investigate the Schatten class membership of the product of a composition operator and the adjoint of another composition operator on the Hardy and Bergman spaces. We provide several sufficient conditions and necessary conditions for these operators to belong to the Schatten classes. Moreover, for some specific symbols including linear fractional maps, finite Blaschke products, and inner functions, we obtain necessary and sufficient conditions.

A solvable microscopic model of interacting electrons in a half-filled Landau level is presented. The Hamiltonian is a well-defined limit of the electron-electron interaction. The low energy sector consists of a set of independent, spatially interlaced, one-dimensional systems of non-interacting fermionic dipoles, each system with a Fermi sea ground state. The total number of dipoles in the set of Fermi seas forming the two-dimensional ground state equals the number of electrons in the system and the density of states at the Fermi level is that of a two-dimensional Fermi gas. The model is obtained by generalizing, or rather adopting, the existing exact solution on a thin, but not too thin, torus to the two-dimensional bulk case.

Corner states are bound by boundary-mass defects, but this geometric anchoring restricts their spatial and internal control. Focusing on twisted bilayers assembled from Chern insulators with opposite Chern numbers, we show that a mass-phase kink carried by a non-Hermitian interlayer mass and an independent imaginary-momentum kink separate the spectral, in-plane, and interlayer control of mass-defect corner states. The mass-phase kink creates the parent corner pole and fixes its energy and intrinsic decay, while directed interlayer tunneling encodes its layer polarization. The imaginary-momentum texture instead reshapes the closed-boundary envelope and redistributes stationary right-state weight between corners. A twisted Qi–Wu–Zhang bilayer verifies this division on arbitrary, including concave, boundaries. A $30^\circ$ twisted Haldane dodecagon realizes twelve finite-energy parent states whose in-gap spectral manifold persists while boundary patterns redistribute its normalized right-subspace weight toward six, three, two, or one target corners. The two kinks therefore cooperate or compete while keeping spectral ancestry, spatial weight, and layer character distinct, thereby establishing a unified framework for controlling mass-defect corner states across disparate boundary geometries and mass textures.

Emil Artin asked whether the left and right dimensions of an extension of skew fields must agree. Cohn and Schofield gave counterexamples through elaborate constructions. It has been a long-standing open question whether there is any division ring, infinite-dimensional over its center, for which the left and right indices agree whenever at least one is finite. We give the first such examples. Call a division ring index-symmetric if every division subring with at least one finite index has equal finite indices. Using a duality formula for bimodules over division algebras, we prove that every twisted Calabi–Yau division algebra is index-symmetric. The examples include the Weyl skew fields and, more generally, the quotient division rings of rings of differential operators on smooth affine varieties in characteristic zero. Further examples are the quotient division rings of enveloping algebras of finite-dimensional Lie algebras, Ore extensions of twisted Calabi–Yau noetherian domains, quantum affine spaces, and group algebras of torsion-free polycyclic-by-finite groups.

FirstFit colors each arriving vertex with the smallest positive integer absent from its previously colored neighborhood. We prove that this rule can require $n^{\Omega(1)}$ many colors on certain bipartite graph of $n$ vertices even when the vertices arrive in a uniformly random order. This refutes the conjecture of Bosek, Gutowski, Lasoń, and Przybyło [BGLP24] that FirstFit uses a polylogarithmic expected number of colors on every bipartite graph in the random order model. We obtain the lower bound by analyzing the FirstFit coloring process on random bipartite graphs, where vertices arrive to either side with equal probability, and with an independent edge density $n^{-x}$ for some $0 < x < 1$. Our result can also be viewed as a qualitative strengthening of Kučera [Kuč91], who showed that, for every $\epsilon > 0$, there are graphs with chromatic number at most $n^{\epsilon}$ on which FirstFit uses $\Omega(n/\log n)$ colors in expectation under a uniformly random order. Our result shows that such poor behavior of FirstFit already occurs for $\chi(G) = 2$.

Image-computable low-level image saliency has shaped perceptual psychology and computer science, but is limited by its inability to capture human high-level cognitive factors that influence attention and eye movements. Here, we propose a new fully automated method to compute semantic saliency by quantifying each object's contribution to scene comprehension without fitting any parameters to human data: the Automated Scene Understanding Map (AUTO-SUM). AUTO-SUM automatically segments and removes individual objects from a scene, uses multimodal large language models (MLLMs) to describe the original and modified scenes, and measures the semantic similarity between these descriptions using text embeddings. We show that AUTO-SUM can predict which object is most important in a human-measured scene understanding map (H-SUM) estimated using human scene descriptions. We also show that AUTO-SUM can predict the object most fixated by human observers during free viewing and scene description tasks better than a low-level saliency model (GBVS, Itti-Koch), a saliency model trained based on human meaning ratings (Meaning Map), and comparable to DeepGaze, which is trained on human fixation data. We contend that AUTO-SUM can be used as a semantic saliency model that complements lower-level saliency models. Code are available at https://github.com/starsky77/AUTO-SUM-Source-Code .

Does evolutionary entropy depend on the width of the age classes used to describe a population? We show that the apparent dependence on temporal resolution is a consequence of the loss of information about reproductive timing within discrete classes. When this information is retained, corresponding continuous and discrete representations yield the same cycle entropy, generation time, evolutionary entropy, and reproductive potential in a common unit of time. When within-class timing is unknown, a uniform local reconstruction yields a logarithmic correction. For constant post-maturity hazard and fertility, continuous exponential and discrete geometric descriptions correspond exactly at every time scale. Thus, for a fixed reference duration, evolutionary entropy is a property of the reproductive process, not of its temporal partition. These results provide a mathematical basis for comparing demographic models across different temporal scales by identifying the information required to separate differences in reproductive organisation from effects of the chosen age-class representation.

We study boundary vanishing orders and asymptotic expansions of planar harmonic functions satisfying the sublinear Robin condition $\partial_\nu u=\lambda u-|u|^{p-1}u,$ with $\lambda\geq0$ and $0<p<1$. For nontrivial global solutions on bounded connected Lipschitz domains, we bound the number of nodal domains by the number of Steklov eigenvalues strictly below $\lambda$ and establish finite vanishing order at every boundary point. The boundary scaling gives the critical exponent $\frac{1}{1-p}$. On $C^1$ boundaries, every positive subcritical vanishing order is an integer, and the leading term is a unique homogeneous Neumann profile in conformal coordinates. At a noninteger critical order, the rescaled solution converges in normalized graph coordinates to an explicit homogeneous profile determined by $p$ up to sign. Every supercritical bulk vanishing order $m$ is an integer, with a unique homogeneous Dirichlet profile in conformal coordinates. The boundary trace has vanishing order $\frac{m-1}{p}>m$. Integer critical vanishing orders are excluded if the boundary is $C^1$ with Dini mean oscillation.

This paper presents the NPU-ASLP music restoration system developed for Track 1 of the China Computer Federation (CCF) Advanced Audio Technology Competition (AATC) 2026 Challenge. The task aims to recover clean music from mobile-device-captured recordings affected by coupled degradations from playback devices, acoustic propagation, environmental noise and recording terminals. System development is further constrained by limited and imperfectly aligned real data pairs and a strict model-complexity budget. In our system, we adopt TF-MoE as the backbone for its dual-axis modeling of cross-band and temporal dependencies, whose Top-1 routing activates a single expert per token to bound computation under the strict budget. We extend it with two task-specific adaptations: a scale-aware encoder and a complex mapping decoder. The former encodes normalized complex spectra jointly with per-band log-RMS to preserve the band-energy cues discarded by band-wise normalization. The latter directly estimates the clean complex spectrum rather than masking the input, thereby repairing coupled degradations. To address the limited, imperfectly aligned real recordings, we further build a challenge-calibrated playback–propagation–recording simulator that generates 1,572.12 h of sample-aligned data across 202 acoustic conditions. The final system contains 2.951M parameters and requires 82.659 GMACs for a 10-s input. On the official blind test, it achieved -49.067 dB SI-SNR, 1.273 LSD, 2.540 FAD, and 3.495 ViSQOL. It ranked third in LSD, FAD, and ViSQOL and received the third prize in the challenge.

With the rapid proliferation of social media, harmful memes have become a growing threat to online ecosystems. Their harmfulness is often implicitly conveyed through complex interactions among visual, textual, and contextual cues, making accurate detection challenging. Recent studies have introduced Retrieval-Augmented Generation (RAG) and external knowledge into harmful meme detection. However, existing methods mainly retrieve similar instances or auxiliary information, limiting their ability to capture reusable harmfulness knowledge and underlying reasoning mechanisms, and thus constraining both detection performance and interpretability. To address these challenges, we propose MemeLogos, a knowledge-driven retrieval-augmented reasoning framework for harmful meme detection. MemeLogos abstracts recurring harmfulness patterns and reasoning structures from diverse harmful cases into reusable knowledge units and organizes them into a dedicated star-shaped knowledge graph. By combining structured knowledge retrieval with an explicit multi-stage reasoning process inspired by cognitive mechanisms, MemeLogos leverages retrieved knowledge to guide harmfulness reasoning, improving both detection reliability and interpretability. Extensive experiments show that MemeLogos consistently outperforms existing harmful meme detection methods while generating more coherent and interpretable reasoning, demonstrating the effectiveness of structured harmfulness knowledge for multimodal content understanding.

Local measurements of gas flow in microscale geometries remain challenging due to the difficulty of micromechanical sensors implantation. Here, we use a levitated nanoparticle as a minimally invasive probe to map, with high spatial resolution, both the local pressure and velocity gas flow for a canonical example - a micropipe subjected to a pressure gradient. This technique enables characterization of nonequilibrium gas transport across several flow regimes, from slip flow to free-molecular flow. We directly observe the emergence of a nonlinear pressure distribution at large pressure ratios and obtain agreement with kinetic-theory predictions and Direct Simulation Monte Carlo calculations. These results introduce levitated nanoparticles as powerful and reconfigurable probes for microchannel gas sensing, with applications in microtechnology, micro-chemistry, and bioengineering.

MDP planners often rely on nominal transition models that may differ from the true dynamics. Robust MDP planning accounts for this uncertainty through a set of admissible models, but doing so with limited online computation is challenging: the search tree grows exponentially with the horizon and each robust backup requires an additional optimization. Existing online robust methods remain limited in scale and offer at most probabilistic guarantees. We introduce, to the best of our knowledge, the first deterministic anytime guarantees for robust online MDP planning. We restrict computation to the sampled search tree while deterministically bounding the contribution of unsampled trajectories. For any fixed policy, we derive lower and upper bounds on the gap between its projected and true robust values under rectangular and non-rectangular uncertainty sets. Under rectangular uncertainty, we propagate these bounds through the robust Bellman operator to bound the optimal robust value. These bounds are computable from the current sampled tree, hold at every node, tighten as the sampled support expands, and converge to the robust values as full support is recovered. We develop CAR-MCTS, a bound-guided MCTS planner that uses these deterministic bounds to guide exploration, prune provably suboptimal branches, and terminate once the optimal root action is certified. The fixed-policy bounds also yield an anytime policy-evaluation mechanism that certifies the robust value of any policy, independent of how it was obtained. Experiments verify the deterministic bounds, their tightening under support expansion, substantial branch pruning, root-action certification, and convergence to the optimal robust policy. To our knowledge, this is the first scalable robust MCTS framework with anytime deterministic guarantees for both online planning and policy evaluation, without enumerating the full state space.

In this paper, we study the focusing mass-critical Hartree equation \[ iu_t+\Delta u=-\bigl(|x|^{-2}*|u|^2\bigr)u \] at the ground-state mass $M(Q)$. We prove that, up to the symmetries of the equation, every global minimal-mass non-scattering solution is a solitary wave, while every finite-time minimal-mass blowup solution is a pseudo-conformal image of a solitary wave. This extends the results of \cite{LZ28,Miao-Xu-Zhao3,Wang-Gao} to the scaling-critical space $L^2$ and removes the radial assumption in the global case.

LLM-based multi-agent systems (LLM-MAS) use specialized agents that exchange messages to accomplish complex tasks. Their reliance on networked protocols, remote tools, and model endpoints exposes communication to message loss, delay, and context expiration. Because agents often exchange open-ended natural language, anomalies can alter task-relevant information while leaving messages processable, allowing semantic errors to propagate through subsequent interactions. Systematic studies of faults in inter-agent communication remain limited. This paper presents a large-scale empirical study of how communication faults manifest, propagate, and affect task outcomes in LLM-MAS. We construct a cross-layer taxonomy linking lower-stack disturbances to application-visible faults and develop a fault-injection and tracing pipeline. Our evaluation covers more than 29,000 executions across 100 tasks, five domains, three workflow topologies, and three model configurations. We find that 20.7% of failures with complete detection records occur without an immediate failure signal, reaching 76.2% for partial-content faults. Flat maintains 53.0% task success under communication faults, compared with 3.3% and 3.2% for Sequential and Hierarchical, respectively. This advantage primarily arises when an alternative information path preserves the evidence required by downstream agents. We also evaluate execution-side and evidence protection mechanisms and find that they recover different failure cases. Evidence recovery depends on whether trustworthy information remains accessible through an unaffected path. These observations provide empirical insights into communication-fault propagation, workflow resilience, and protection design for LLM-MAS.

Existing analyses of interval length in split conformal prediction largely focus on clean data. However, how contamination at the training and calibration stages alters interval length relative to the corresponding clean population oracle remains understudied. In this paper, we consider Huber contamination and derive a finite-sample upper bound that holds uniformly over contaminating distributions, with leading terms scaling as $L(\delta_1+n_1^{-1/2}) +(n_2^{-1/2}+\delta_2)/((1-\delta_2)r_0)$, in addition to a clean-sample estimation term. We further establish a minimax lower bound matching the upper-bound rate up to constant factors on a regular asymmetric location submodel. For calibration contamination, we obtain an exact worst-case characterization of the population interval-length deviation. We also extend the upper-bound results to conformalized quantile regression and adaptive residual scores. Experiments on synthetic and real-world datasets provide empirical support for our theoretical findings on training and calibration contamination.

We give new proofs of interior second derivative estimates for the Monge-Ampère equation and the constant quadratic Hessian equation, based on the two-point maximum principle. The arguments require only one differentiation of the equation. For the Monge-Ampère equation, the inhomogeneous term is assumed to be positive and continuously differentiable. For the quadratic Hessian equation, the estimate holds in every dimension $n\ge2$.

Accurate, physiologically consistent glucose forecasts could help people with type 1 diabetes respond to impending excursions. We applied our physiological-model-based neural network (PMB–NN) framework to glucose forecasting. A temporal convolutional network (TCN) used 180 min of history, constrained during training by a personalized four-parameter physiological model. The main PMB–NN combined forecast and neural–physiological agreement losses; a three-term variant additionally fitted physiological predictions to measured glucose. Data comprised 6–8 weeks of continuous glucose monitoring, pump, and meal records from 25 AZT1D participants. Person-specific models used chronological 70/10/20 train/validation/test splits and 30-, 60-, and 120-min horizons. Median mean absolute errors were 16.24, 25.00, and 30.20 mg/dL with basal insulin records and 15.38, 24.21, and 31.79 mg/dL before these records became available. In the latter setting, PMB–NN had the lowest median error at 30 and 60 min; it outperformed the physiological model alone in all six settings. In input-increase tests, glucose predictions changed in the expected direction for 85% of correction boluses and 100% of carbohydrate rescues, versus 57% for active insulin and 56% for active carbohydrates. Most standalone physiological fits showed locally distinguishable parameter effects, with glucose-related coefficients more stable under resampling than insulin- or carbohydrate-related coefficients. The three-term variant improved hyperglycaemia accuracy with basal records, but did not significantly change overall MAE and reduced directional plausibility in three tests. PMB–NN combines personalized forecasting with an explicit physiological model, allowing assessment of predictive accuracy, physiological response behavior, and participant-specific coefficients.

In multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) systems, conventional receivers based on linear channel estimation and subband-averaged interference covariance reconstruction suffer serious performance degradation under strong interference. To address this issue, we propose a probabilistic framework for joint channel estimation and interference suppression using score-based prior learning. Specifically, we formulate a variational inference problem that exploits the bilinear structure of the interference by explicitly separating the interference channels from the interference symbols. To solve the resulting highly nonconvex bilinear inference problem, we develop a score-based variational inference algorithm that combines score-based turbo message passing for target-channel estimation with a reverse mean propagation framework for interference-channel inference, while the interference symbols are updated via linear minimum mean square error (LMMSE) estimation. We further design an interference rejection combining (IRC) detector with subcarrier-level covariance reconstruction based on the estimated interference channels, thereby avoiding the performance loss caused by conventional subband averaging. Numerical results demonstrate that the proposed algorithm is able to effectively suppress the interference in channel estimation, as well as to accurately reconstruct the interference subspace for interference rejection in data detection, and thus significantly outperforms existing baselines.

We prove that a commutative integral domain is Gorenstein Prüfer if and only if every overring is Gorenstein flat over the original domain. It is enough to test overrings that are finitely generated as algebras. The proof combines finite duality with a conductor-quotient argument. Under the overring hypothesis, the conductor quotient of a proper overring generated by two elements as a module is an IF-ring, and degree-one duality lifts first syzygies of finitely presented quotient modules to totally reflexive modules. This gives a bound of one for the Gorenstein flat dimension of every module annihilated elementwise by conductor powers. Quadratic integral elements provide such conductors at nonnormal localizations, while normal localizations give principal-ideal neighborhoods. Constructible compactness yields a finite cover, and a bounded complex of localizations combines these bounds over the original domain. Consequently every finitely generated ideal is Gorenstein flat and the domain is coherent. Examples distinguish finite-type from module-finite tests and Gorenstein flatness from ordinary flatness.