Papers

Natural sanidine commonly preserves metastable chemical disorder at ambient conditions, but the local structural correlations associated with this disorder remain poorly understood due to a reliance on average-structure analysis alone. Here, we investigate single-crystal diffuse scattering in a natural sanidine from Drachenfels, Germany, with consistent observations across additional samples from Laacher See, Germany, and Vesuvio, Italy. The diffraction data reveal pronounced anisotropic diffuse features, including characteristic bowtie-like intensity distributions in reciprocal space. To resolve the origin of these features, we combine three-dimensional difference pair distribution function (3D-$\Delta$PDF) analysis with force-field calculations and Monte Carlo modelling. The 3D-$\Delta$PDF shows correlated deviations from the average structure and indicates a strong coupling between occupational and displacive disorder. Force-field calculations demonstrate that the aluminosilicate framework responds strongly to the local alkali occupancy, with the largest structural variation occurring along the $a$ direction. Guided by these observations, we construct a disorder model in which K/Na occupational short-range order is combined with chemically constrained Al/Si distributions and local framework relaxations. The model reproduces the main experimental diffuse-scattering features and shows that the bowtie-like diffuse scattering arises from correlated framework distortions driven primarily by local K/Na order.

Yang introduced a tempered xi function $\widehat\xi(s)$ by replacing the hyperbolic cosine in a classical integral representation of the Riemann xi function by a hyperbolic sine, and conjectured that every zero of $\widehat\xi$ lies on the critical line $\Re s=1/2$. We disprove this conjecture. After the change of variables $x=e^{2t}$, one has \[ \widehat\xi\!\left(\tfrac12+iz\right)=iS(z), \qquad S(z)=\int_0^\infty K(t)\sin(zt)\,dt, \] where $K$ is positive, smooth, and doubly exponentially decaying. Two integrations by parts give $S(y)=K(0)/y+O(y^{-2})$ for real $|y|\to\infty$, with $K(0)>0$; hence $S$ has only finitely many real zeros. On the other hand $S$ is an entire function of order at most one. If it had only finitely many zeros in the complex plane, Hadamard factorization would force $S(z)=P(z)e^{az+b}$, which is incompatible with $S(y)\to0$ as $y\to\pm\infty$. Thus $S$ has infinitely many nonreal zeros, and consequently $\widehat\xi$ has infinitely many zeros off the critical line. The proof is unconditional and does not use the Riemann Hypothesis or numerical zero finding. A short numerical illustration is included.

We study the Schatten class membership and essential norms of the operators $C_\varphi C_\psi^*$ and $C_\psi^*C_\varphi$, where $C_\varphi$ and $C_\psi$ are composition operators with nonconstant linear fractional symbols, acting on weighted Dirichlet spaces $\mathcal{D}_\alpha$ with $\alpha>-1$. We obtain complete characterizations of their Schatten class membership in terms of the boundary behavior of $\varphi$ and $\psi$. In particular, the corresponding geometric conditions are independent of the Schatten exponent, and each product belongs to every Schatten class whenever its boundary condition is satisfied. We also investigate the essential norms of these products. For $\alpha=0$ and $\alpha>0$, we obtain exact formulas in terms of boundary contact and the derivatives of the symbols, while for $-1<\alpha<0$ we obtain two-sided estimates by reducing the problem to positive Toeplitz operators and local averages of generalized Nevanlinna counting functions.

Collective modes in a superconductor correspond to fluctuations in the amplitude (Higgs mode) or the phase (Goldstone mode) of the order parameter. Starting from the BCS Hamiltonian, we derive a microscopic Hamiltonian for the coupled Higgs-Goldstone-electron system that contains all interactions among these degrees of freedom. The Higgs subsystem is a weakly interacting Bose gas: Higgs modes experience a mutual attraction mediated by the virtual exchange of Bogoliubov quasi-particle pairs. They also interact with external electromagnetic-fields with a coupling constant that we derive explicitly. We use this theory to examine whether an optically pumped gas of Higgs modes can undergo Bose-Einstein condensation. We identify a density window, bounded below by the equilibrium condensation criterion and above by collapse due to the attractive interaction, in which condensation can occur and we derive the expected density of Higgs-modes due to external pumping. This pumping depends crucially on non-parabolic corrections to the electron dispersion around the Fermi-energy. We show that the pumped mode density is compatible with condensation for realistic material parameters. We suggest possible experimental signatures of this non-equilibrium condensate.

Classical soft theorems govern the non-analytic structure of electromagnetic and gravitational radiation in the low-frequency regime, with the gravitational memory effect providing the canonical realization of the classical soft graviton theorem. While the soft behavior of radiation from hyperbolic scattering is well understood, its realization in gravitationally bound systems remains less explored. In this work, we study the soft structure of gravitational waveforms generated by compact binaries, focusing on the scattering of emitted radiation off the static background curvature within the multipolar post-Newtonian framework. We isolate the infrared (IR) logarithms associated with hereditary effects, including the tail-of-memory, and their higher generalizations with n-tail insertions. The resulting amplitudes exhibit a Laurent expansion in frequency space consistent with the Sahoo-Sen logarithmic soft theorems, thereby establishing a direct correspondence between gravitational memory effects, their higher-order tail corrections, and the soft expansion. We also comment on ultraviolet (UV) logarithms arising from short-distance sensitivity of the multipole expansion and their associated renormalization-group running.

The speed v(lambda) of the lambda-biased random walk on a supercritical Galton-Watson tree without leaves is conjectured to be nonincreasing on [0,m), where m is the mean offspring. For non-constant offspring, monotonicity is known only for small bias: lambda <= 1/1160, lambda <= 1/2, and, when every vertex has at least m_1 >= 2 children, lambda <= m_1/(1+sqrt(1-1/m_1)). For offspring uniform on {2,3} (m=2.5) the last bound is 2/(1+sqrt(1/2)) = 1.17157... We prove, with computer assistance, that v is strictly decreasing on [0,1.755] for this law. The proof has three parts. Aidekon's speed formula gives v=(R-lambda)/(R+lambda) for an explicit functional R, so v decreases exactly when R/lambda does; we compare R/lambda at two biases directly, which avoids differentiating the conductance. A pathwise Lipschitz bound on the conductance in lambda turns that comparison into an inequality between expectations of explicit functions. A monotone sandwich of discretised laws gives two-sided bounds on the conductance law, and each lambda-cell is verified with exact rational arithmetic on top of bounded floating-point error; an independent interval-arithmetic implementation re-certifies five cells, including the one that sets the endpoint. The method stops where the crude Lipschitz bound becomes too weak; sharper control of the derivative of the conductance is what the full range needs. Code and certificates are public.

Survey responses are often measured using ordered response categories. In the European Social Survey, self-rated health is measured on a five-point scale from very good to very bad, yet analyses commonly dichotomise responses into binary categories of "good" and "poor" health. Binary indicators provide prevalence measures that are straightforward to communicate, but dichotomisation reduces information and may limit captured health variation, while the cut-off may influence estimates and substantive conclusions. Systematic evidence on these effects in spatial settings remains limited. We address this gap using European Social Survey round 11 (2023/2024) for Western Europe. We model self-rated health among male respondents by age, education and region. Bayesian spatial individual-level models with poststratification provide population-representative estimates. We compare an ordinal cumulative logit model for the five-category outcome with Bernoulli logistic regression models using two dichotomisations differing in the classification of "fair" health. Older age and lower education are consistently associated with worse self-rated health across specifications, suggesting relatively robust fundamental age and educational gradients. However, their magnitude and uncertainty, and some geographical conclusions, are sensitive to how the outcome is modelled. Assigning "fair" health to either side of a binary cut-off changes the regions identified as having above-average levels of less favourable health. The ordinal model retains category-specific information and can produce familiar binary prevalence estimates through aggregation. Binary indicators remain useful, particularly for monitoring and communication. Nevertheless, the selected cut-off should be justified and sensitivity to alternative cut-offs or an ordinal modelling approach should be considered, especially for geographical comparisons.

The rapid progression of large language models is extending AI from passive content generation into the active workflows of engineering and scientific discovery. This shift raises a compelling question: can AI be both the object of development and an active participant in building next-generation AI systems? We explore this question by building Qwen-Planner-Agent within a closed-loop AI-for-AI framework for scalable development and iterative improvement. Mobile planning offers a demanding test of this approach: complex, long-horizon tasks challenge agent reliability, while costly real-device interaction limits development scalability. The framework connects data production, model training, and deployment through a shared action-feedback-verification contract. (i) AI for Data builds a human-gated agentic data flywheel in which specialized agents construct tasks, collect interaction trajectories, curate and balance training data, and use training feedback to guide subsequent data generation. (ii) AI for Training combines a supervised planning cold start with hybrid-environment online agentic reinforcement learning, where we introduce Competence-Aware Reward-and-Advantage Engineering (CARE) to reduce reasoning and tool-use costs while preserving task performance. (iii) AI drives model–harness co-evolution through an execution-evidence-driven loop that orchestrates memory, skills, and tools at runtime and feeds structured action feedback and preserved failure traces back into coordinated model and harness adaptation. Qwen-Planner-Agent achieves the best overall performance among all evaluated models and systems on MobilePA-Bench, improving over its base model across tool use, memory, skills, and sub-agent coordination. Further evaluations of our model show improvements across non-mobile agentic benchmarks while largely preserving general capabilities.

The classical Becker-Döring equations describe the formation of clusters by aggregation and fragmentation of monomers. If the total amount of mass is supercritical, larger and larger clusters are formed, leading to an asymptotic loss of mass in the long time limit. The two-component Becker-Döring system arises when clusters are built from two types of monomers. Here, we study the natural extension of the one-component system, where no energy or entropy is leaving or entering the system - the so called detailed balance assumption. We rigorously prove that all initial conditions admit a solution minimising the relative entropy as time approaches infinity. This shows, that the long time limit in the weak* topology is selected through the initial Type I and Type II masses. Furthermore, the proportion of lost Type I mass is determined by the limit point via the mixing ratio of Type I and Type II monomers that maximises the binding energy. The main difficulty of the two-component system is that no relative entropy is weak* continuous, which is crucial for the classical argument [2]. Instead, our proof is based on a discrete two-dimensional logarithmic Sobolev inequality, that bounds the entropy dissipation on the correct timescale. Our approach also improves current assumptions to determine the long time behaviour for the one-component system.

Non-Clifford gates are essential for universal quantum computation, yet implementing them fault-tolerantly remains a central challenge for stabilizer codes. Here, we show how a syndrome degree of freedom can mediate a logical non-Clifford gate. Releasing one stabilizer check makes an additional logical qubit available within the encoded data block. Two Pauli rotations, followed by syndrome measurement and Clifford feed-forward, then implement a deterministic logical $T$ gate on every stabilizer code of distance at least two, in a suitable logical basis. During the ideal rotations, the state remains in an intermediate stabilizer code whose distance we determine exactly. For pure codes with a balanced factorization, this distance grows with the original code distance, whereas the maximum weight of the stabilizer generators bounds the intermediate distance from above. We realize the mechanism in two circuits that tolerate a single fault under local stochastic circuit noise: a fixed 22-qubit construction admitting recursive error suppression and a direct Golay-code gate protected by measuring a stabilizer check transported through the non-Clifford rotation, which can recover the unknown encoded state even after rejection. Serial implementations with ancilla reuse, reset, and flexible two-qubit connectivity require at most 33 and 32 physical qubits, respectively. These results establish a general mechanism for logical non-Clifford gates and demonstrate how syndrome measurements and recovery can protect the intermediate evolution of encoded information.

Recent non-autoregressive (NAR) zero-shot text-to-speech (TTS) models generate in parallel but typically require the target sequence length to be specified before generation. We introduce EditVoice, to our knowledge the first variable-length NAR zero-shot TTS model, which uses Edit Flows to jointly update speech content and sequence length through insertions, deletions, and substitutions. EditVoice adopts speech-infilling training, which unifies zero-shot TTS and text-based speech editing and allows both prefix and suffix speech prompt placements at inference. We introduce Complementary Prompt Sampling (CPS) to leverage the complementary Edit Flow predictions induced by the two prompt placements. We further find that EditVoice can edit source and model-generated speech beyond its training sources. We use this generalization for end-to-end editing and training-free post-generation refinement. With the Edit Flow model trained on 10K h of GigaSpeech, EditVoice demonstrates competitive zero-shot TTS performance on Seed-TTS Eval EN and LibriSpeech-PC and speech editing performance on RealEdit.

We develop randomized branch methods for finding Bouligand-stationary (B-stationary) points of linear and quadratic programs with complementarity constraints (LPCCs and QPCCs) using only linear programming subproblems. The methods exploit the finite-union geometry of the feasible set and search for first-order descent on randomly selected compatible branches. For LPCCs, an exact method optimizes over sampled branches, while an inexact simplex method can accept an improving branch-feasible vertex before solving the sampled penalty problem to optimality. For QPCCs, including problems with indefinite quadratic objectives, branch quadratic programs are replaced by linearized trust-region subproblems; a ratio test ensures actual decrease, and thresholded sampling detects branches that emerge only at accumulation points. Under the stated assumptions, the LPCC methods stabilize after finitely many changes at B-stationary points almost surely. For the QPCC method, finite termination yields a B-stationary point, and every accumulation point of an infinite run is B-stationary almost surely. Experiments on bilevel-induced instances, instances arising from inverse quadratic programming, and sparse affine generalized Nash equilibrium instances, together with 129 MacMPEC embedding tests, show that the methods return points with competitive objective quality and runtimes on large-scale complementarity systems.

This paper investigates cost-sensitive online window size selection for portfolio management under changing market conditions. Specifically, we propose a two-level framework that constructs portfolios using candidate window sizes and dynamically aggregates them through online learning. By treating candidate window sizes as “experts,” we dynamically update their aggregation weights using turnover-inclusive losses. Moreover, we derive finite-horizon cost-sensitive tracking-regret bounds that account for turnover of the aggregated portfolio, with static regret as a special case. Under bounded losses and cost rates, suitably tuned Fixed Share achieves asymptotically no tracking regret for sublinear switching budgets, with Hedge covering the static case.

We present first predictions from the saturation-physics-based framework IP-Glasma for the nuclear modification factor $R_{AB}$ as a function of centrality in $p$ + O, $p$ + Pb, O + O, and Pb + Pb collisions due only to initial-state effects. The same framework is responsible for both soft ($p_T \lesssim 3 ~\mathrm{GeV}$) and semi-hard ($5 ~\mathrm{GeV} \lesssim p_T \lesssim 20 ~\mathrm{GeV}$) particle production, enabling the study of initial-state correlations between bulk and intermediate-$p_T$ particle production from a first-principles framework. We show that, tuned only to HERA data, IP-Glasma accurately predicts the self-normalized multiplicity distributions in $p$ + O, $p$ + Pb, O + O, and Pb + Pb collisions; the minimum-bias nuclear modification factor in $p$ + O and $p$ + Pb collisions; the centrality-cut nuclear modification factor in $p$ + Pb collisions; and the anomalous suppression of $R_{AA}$ observed in very peripheral Pb + Pb collisions. We find that IP-Glasma predicts significantly less suppression than is measured in both $\sqrt{s_{NN}} = 5.36 ~\mathrm{TeV}$ O + O and $\sqrt{s_{NN}} = 5.02 ~\mathrm{TeV}$ Pb + Pb collisions at the Large Hadron Collider, in qualitative agreement with the scenario in which $R_{AA} < 1$ is due to final-state energy loss. We show that the inelastic nucleon-nucleon cross section ($\sigma_{\text{inel}}^{NN}$) produced by IP-Glasma is extremely sensitive to the area of the subnucleonic hotspots; the same values of the hotspot area that reproduce the measured $\sigma_{\text{inel}}^{NN}$ also reproduce minimum-bias $R_{pA}$. Finally, we show that the hard-soft correlations in IP-Glasma arise from event-by-event fluctuations in the color fields, which simultaneously drive enhanced production of both soft and hard particles.

We show that the regularized channel Rényi divergence is continuous at $\alpha = 1$. As consequences, we establish an exponentially strong converse for channel discrimination, a subchannel-smoothed asymptotic equipartition property, a relative entropy accumulation theorem, and a new proof of the generalized quantum Stein's lemma. Our result further shows that the regularized channel relative entropy is computable. The continuity proof relies on a variational formula that expresses the regularized channel divergence as a single-letter optimization over variables of unrestricted finite dimension. We then establish continuity using a novel spectral confinement technique.

Temporary occupation of qutrit levels can reduce the width and depth required for binary circuit logic in quantum computing. We introduce an efficient intermediate-qutrit decomposition of multi-controlled Toffoli gates with binary-subspace inputs and outputs. For balanced control widths $n=2^h-1$, the proposed decomposition is evaluated hierarchically through a tree, allowing independent subtree computations to proceed in parallel and reducing the depth from linear to logarithmic. The balanced low-depth construction requires $6n+3$ logical $P_9$ injections and $\frac{n-3}{4}$ clean ancillary qutrits. It matches the direct $P_9$ count of a recursively extended Clifford+$P_9$ baseline derived from the state-of-the-art work while using asymptotically one-quarter as many clean ancillas and replacing linear depth with logarithmic depth. For arbitrary control widths, a sequential extension preserves the $6n+3$ $P_9$ count but has depth $O(\log m+n-m)$ for a balanced core $m=2^h-1\leq n$, which is linear in the worst case over $n$. By reducing the resource overhead of a widely used reversible primitive, the proposed decomposition provides a practical building block for the design and compilation of more resource-efficient quantum algorithms in the fault-tolerant regime.

This paper is concerned with a no-flux initial-boundary value problem for the degenerate volume-filling chemotaxis system with source terms, \begin{align*} u_t = \nabla \cdot (D(u,v) \nabla u - h(u,v) \nabla v) + f(x, u, v), \quad v_t = \Delta v + g(u,v), \quad x\in \Omega, \ t>0 \end{align*} in a smoothly bounded domain $\Omega \subset \mathbb{R}^N$ $(N \in \mathbb{N})$. It is shown that when $D$, $h$, $f$ and $g$ satisfy suitable assumptions involving $D(1,\cdot)=h(0,\cdot)=h(1,\cdot)=f(\cdot,0,\cdot) = f(\cdot,1,\cdot) = 0$, for nonnegative initial data $u_0$ and $v_0$ with $u_0\le 1$, there exists a global weak solution $(u, v)$ with $u\le 1$. In addition, uniqueness of global weak solutions is established when $D(r,s) = D(r)$ for all $r\in[0,1]$ and $s\in[0,\infty)$, and $D$, $h$, $f$, $g$ and $v_0$ are supposed to satisfy additional conditions.

We identify the optimal constant and describe all maximizers for the Fourier endpoint extension inequality associated with the moment curve over finite fields. This confirms a conjecture proposed in the authors' earlier work. The proof proceeds by showing that the problem is equivalent to a purely probabilistic extremal statement: among all probability distributions on a finite set, the uniform distribution uniquely maximizes the expected number of distinct rearrangements of an i.i.d. sample.

Choosing Shellsort gaps is a well-known open problem. For over sixty years, successful sequences have relied on human-designed formulas, numerical searches, or number-theoretic constructions. Although stronger general bounds exist for dense or mainly theoretical families, the worst-case upper bound for a short, sparse, and practically competitive construction has not advanced beyond $N^{4/3}$ for decades. We ask whether the sequence itself can instead be learned from execution. We present an RL-driven, self-supervised system that searches over executable gap generators. Every proposal is valid by construction, and executed candidates return exact comparison and move counts; no classical sequence is used as a target. Across five independent searches, the system discovers a common rational-geometric family. A second self-supervised stage tunes only a finite prefix, producing the practical sequence $1,3,8,20,47,116,300,585,1416,3303,\ldots$. Once frozen, it obtains the lowest equal-task average operation count among seven classical baselines on 25 large tasks with $10^7<N\leq 10^8$. We complete the learned tail without changing its practical behavior: only beyond $10^{1000}$, a zero-density set of unit companions $h_s+1$ removes the remaining congruence barriers. The resulting sparse sequence has matching polynomial upper and lower exponents, up to polylogarithmic factors: $\Omega(N^{1.024296451657\ldots}) \leq T(N) \leq O(N^{1.024296451657\ldots}\operatorname{polylog} N)$. The lower bound follows from Zang's recent theorem for rational-geometric sequences; our contribution is the matching upper bound. Thus one exact sequence connects self-supervised discovery, large-scale practical performance, and a substantial step below the classical $N^{4/3}$ bound for sparse practical Shellsort sequences.

Mobile crowdsensing (MCS) is a promising enabler of Sensing-as-a-Service (SaaS) for next generation networks (NGNs), where sensing, communication, and computing are jointly considered as on-demand services. In MCS, mobile units (MUs) collect and deliver sensing data to data requesters (DRs) via a mobile crowdsensing platform (MCSP) in exchange for monetary incentives. After sensing tasks are announced, MUs strategically select tasks to maximize their long-term utility while accounting for energy and time costs, whereas the MCSP assigns tasks to maximize its own service revenue and data quality. A fundamental challenge arises from the lack of prior knowledge of MUs' sensing qualities and task efforts, as well as the energy limitations of battery-powered devices, which directly impacts service availability and reliability in SaaS for NGNs. To address these challenges, we formulate the interaction between MUs and the MCSP as a dynamic two-sided matching game under incomplete information, explicitly incorporating energy constraints. We propose Energy-aware Two-Sided Learning (ETSL), a fully decentralized and lightweight learning framework in which MUs locally learn task proposal strategies, while the MCSP learns the data quality of participating MUs to devise task assignment strategy. ETSL jointly enables MUs' energy-aware task proposals and MCSP's adaptive task assignment, considering their individual preferences to maximize their net revenues. Simulation results demonstrate that ETSL significantly improves MU and MCSP profits and overall energy efficiency, highlighting its effectiveness as a scalable and sustainable SaaS solution for NGN.

Generative modeling approaches often focus on recovering broad statistical characteristics from the training data. In the context of graph generation, this may refer to degree distributions, clustering coefficients, or spectral properties. However, generating usable distribution feeders when detailed feeder models are unavailable requires more than matching generic graph statistics: the sampled topology must also obey electrical compatibility and radiality rules. We therefore formulate feeder synthesis as a constraint-guided graph generation problem and propose the Power-Grid-constrained Discrete Denoising Diffusion model, PG-DiGress, which learns categorical node and edge patterns from feeder data, while respecting domain-specific rules. Specifically, it injects feeder constraints into the reverse diffusion process through soft masks that suppress incompatible edge classes during denoising, followed by a final projection step that rebuilds a connected, rule-compliant feeder graph. We evaluate PG-DiGress using graph-distribution similarity, feeder-rule satisfaction, structural validity, and downstream model construction. Compared with the unconstrained baseline, PG-DiGress increases the strict feeder pass rate from 13.7% to 96.8%. We also successfully convert the generated graphs into executable feeder models for downstream analysis.

The Davenport constant $\DD(G)$ of a finite abelian group $G$ is a classical invariant arising from the arithmetic of ideal class groups of number fields. Closely related to the Davenport constant is the first Narkiewicz constant $\Nark_1(G)$, which arises in the quantitative study of algebraic integers and their factorizations. Gao and Geroldinger conjectured in 2006 that $\DD(G)\leq \sum_{i=1}^r n_i,$ while Narkiewicz and Śliwa conjectured in 1982 that $\Nark_1(G)=\sum_{i=1}^r n_i,$ where $n_1,\ldots,n_r$ are the invariant factors of $G$. Both are central conjectures concerning arithmetic invariants arising from the theory of number fields. In this paper, we disprove both conjectures. Moreover, we show that, for every fixed $r\geq5$, both $\DD(G)-\sum_{i=1}^r n_i$ and $\Nark_1(G)-\sum_{i=1}^r n_i$ are unbounded over finite abelian groups of rank $r$. We develop a probabilistic representation technique to establish a uniform upper bound for the Davenport constant: $$ \DD(G)\leq\frac{16}{5}\,\rr(G)\exp(G). $$ Our bound gives the first improvement of the classical van Emde Boas–Kruyswijk estimate: $\DD(G)\leq\exp(G) \left(1+\log\frac{|G|}{\exp(G)}\right) \leq\exp(G)\bigl(1+(\rr(G)-1)\log\exp(G)\bigr)$, by removing the logarithmic dependence on the exponent from this classical estimate, replacing it with the absolute constant $16/5$. Their bound stood unimproved since its establishment in 1969. The existence of $C=16/5$ also brings us closer to the most challenging conjecture on the Davenport constant, namely the Emde Boas–Kruyswijk Conjecture in 1969, which predicts that $\DD(C_n^r)=r(n-1)+1.$ As a further application of our results, we disprove a conjecture of Girard in 2008 concerning cross numbers, an invariant with deep roots in the arithmetic of number fields and Krull monoids.

The degrees of the iterates of a projective endomorphism grow in two layers: an exponential rate measured by the dynamical degrees, and a polynomial correction carried by the peripheral Jordan blocks. Log-concavity constrains the first layer; we show that the Hodge index theorem already constrains the second, in every codimension and in arbitrary characteristic. Let $f$ be a surjective endomorphism of a normal projective $d$-fold over an algebraically closed field, with dynamical degrees $\lambda_i$, so that $\textrm{deg}_i(f^n)\asymp\lambda_i^n n^{\mu_i}$ for a unique integer $\mu_i\ge0$. We prove that these exponents are coupled across three adjacent codimensions: strict log-concavity of $(\lambda_i)_i$ at $i$ forces $\mu_i=0$, while equality gives \[ 0\ \le\ 2\mu_i-\mu_{i-1}-\mu_{i+1}\ \le\ 4 . \] Consequently, $\mu_i\le2i(d-i)$, and this is sharp for every $i$. For a zero-entropy automorphism, we prove that every mixed orbit function indexed by any weak composition $\gamma$ of $d$ is a multivariate quasipolynomial of even total degree at most $d^2-\sum_j\gamma_j^2$. For a zero-entropy holomorphic automorphism $g$ of a compact Kähler $d$-fold $Y$, the same method gives \[\left\|(g^n)^*|_{H^{p,q}(Y,\mathbb{C})}\right\| =O\bigl(n^{p(d-p)+q(d-q)}\bigr).\] Powers of elliptic curves attain all exponent bounds as well as the constant $4$.

Neurosymbolic research typically assumes a pre-existing symbolic specification, leaving the upstream challenge of acquiring and formalizing requirements and constraints largely unaddressed. We present an architecture that fills this gap by using an OWL configuration ontology to mediate between neural constraint sources and downstream consumers. In this framework, LLM assistants elicit soft stakeholder preferences, while hardware specifications define hard physical and engineering limits. The ontology unifies these heterogeneous inputs, leverages description logic to identify unsatisfiability, and generates symbolic explanations that enable LLMs to interactively renegotiate terms with users. Any remaining conflicts are resolved downstream via priority-based relaxation. We illustrate our approach on a microgrid use case from the FLEXI project and argue its generalizability to multi-stakeholder domains where constraint acquisition is distributed across human and automated sources of unequal authority.

Long horizon language model agents continually accumulate reasoning history, increasing context length and inference cost even after earlier decisions have been executed and observed. Unlike static Chain of Thought compression, removing historical reasoning can change future actions and the resulting interaction trajectory. We study when such reasoning can be safely forgotten. We propose Interaction Aware Compression for Long Horizon Reasoning (ICLR), a training free online method that ranks reasoning blocks using frozen proxy entropy while preserving actions, tool calls, and observations. On 260 WorkBuddyBench tasks, ICLR improves average reward from 0.699 to 0.718, while reducing input, output, and cache read tokens by 25.5%, 14.4%, and 33.3%, respectively. Ablations reveal trajectory amplification, where local reasoning deletion produces nonlinear changes in total computation by altering subsequent interaction. Representation probing, activation patching, and controlled trajectory analyses further suggest that historical reasoning becomes more replaceable once task relevant derived state has been reliably externalized into code, files, tool outputs, or environmental feedback. These results characterize agent reasoning as dynamic working state rather than permanent interaction history.

Generative artificial intelligence can turn learning analytics into personalized support, but feedback systems must decide when to intervene, which evidence to use, and how much assistance to provide. We developed a risk-adaptive, evidence-constrained framework for introductory programming using 2993 failed-submission states from 215 students. Student-disjoint models predicted persistent failure and related outcomes; four matched feedback conditions were generated for 136 cases; and calibrated risk informed capacity-limited intervention policies. The validation-selected logistic regression model achieved a test precision-recall area under the curve of 0.550 and a receiver operating characteristic area under the curve of 0.681. Broader student histories improved prediction of unmodified resubmission. After standardized repair and evidence gating, 519 of 544 newly generated messages contained all required components. A fixed-threshold sequential policy selected 17.8% of eligible test states and captured 25.2% of observed persistent failures. These findings support an evidence-gated progressive assistance strategy: calibrated risk guides intervention timing, recorded evidence constrains feedback content, and assistance progresses from self-checks to localized hints when warranted. The framework connects prediction, decision-making, and grounded generation while keeping their evaluation outcomes distinct.

S4 0954+65 (4FGL J0958.7+6534) is a TeV-detected blazar at a redshift of $z = 0.3694 \pm 0.0011$, classified as an intermediate-synchrotron-peaked BL Lac object. In early 2025, it entered an exceptional $\gamma$-ray high state. We aim to investigate the origin and physical properties of the exceptional 2025 flare, and to constrain the emission processes responsible for this flaring activity. We performed a multi-wavelength analysis using $\gamma$-ray, X-ray, optical/UV, radio, and 43 GHz Very Long Baseline Array (VLBA) observations. We examined multi-band correlations with the z-transformed discrete correlation function (zDCF), analyzed the spectral evolution and parsec-scale jet kinematics, and modeled the broadband spectral energy distributions (SEDs). The $\gamma$-ray variations lead the optical and radio emission by 3.22 days and possibly 18.26 days, respectively, while no significant correlation is found between the $\gamma$-ray and X-ray emission. The $\gamma$-ray spectra show a harder-when-brighter behavior, consistent with enhanced particle acceleration during the active state. A similar spectral trend is also observed in the X-ray band, where the photon index is anti-correlated with flux. During the major $\gamma$-ray flare, VLBA images reveal the emergence of a new superluminal radio knot from the core, whose extrapolated ejection time is consistent with the peak of the $\gamma$-ray flare. The temporal and structural evolution during the 2025 flare is consistent with a shock-in-jet scenario, in which a newly emerging disturbance propagates downstream and drives the flare. Broadband SED modeling shows that a leptonic synchrotron self-Compton plus external Compton model with dusty torus seed photons reproduces the multi-wavelength observations with physically plausible parameters. A lepto-hadronic interpretation remains possible but requires substantially higher jet power.

Asymptotic cohomology was recently introduced to study stability problems in group theory. This paper studies vanishing and Hausdorffness questions around asymptotic cohomology. Our first main result is that, in a fixed degree and for a fixed asymptotic coefficient module, vanishing of asymptotic cohomology is equivalent to vanishing of reduced asymptotic cohomology. In the special case of diagonal coefficient modules, we also obtain a full characterisation of vanishing in terms of bounded cohomology. Our second main result is that asymptotic cohomology vanishes in degree 1 for uniformly convex asymptotic Banach modules. From this, we can deduce Hausdorffness of degree-2 bounded cohomology under the same uniform convexity assumption.

Slow magnetoacoustic pulsations (SMAPs) are found in MHD simulations of a tokamak plasma whose safety factor $q$ near the center is flat and slightly above unity ($q \gtrsim 1$). SMAPs are located on the central plateau of the slow magnetoacoustic continuum $\omega_{\rm S} = k_\parallel c_{\rm S}$, where $c_{\rm S}$ is the speed of sound and $k_\parallel$ the wavenumber parallel to the magnetic field. In our model, SMAPs exist when the ion viscosity and thermal diffusivity are sufficiently low. They can be driven unstable by a pressure gradient in the $q \sim 1$ region when the electric resistivity is sufficiently high. Exponentially growing SMAPs consist of standing slow waves on magnetic surfaces that are radially synchronized into a quasi-interchange structure with poloidal/toroidal mode numbers $m/n=1/1$. After free energy depletion, saturated quasi-linear pulsations (alternating $n=1$ and $0$) in the central $q\sim 1$ region couple to distant $q\geq 2$ rational surfaces that undergo "reversible" magnetic reconnection: as the magnetic islands wax and wane with period $2\pi/\omega_{\rm S}$, their X- and O-points alternate. These results show how the MHD model facilitates non-local coupling of slow waves, pressure-driven resistive interchange and tearing. This motivates further study in kinetic models, where collisionless mechanisms for fast reversible reconnection exist and proper treatment of parallel dynamics will allow to assess the role of Landau damping as well as the question whether the ${\mathbf B}$ field's weak ergodicity in the $q\sim 1$ region allows the waves to outpace the ion's parallel streaming to maintain the thermal misbalance underlying SMAPs. Also of interest are pulsations closer to the Alfvénic branch, satisfying $\omega \approx k_\parallel v_{\rm A}$ with Alfvén speed $v_{\rm A}$, which require no resistivity and are less dependent on thermal misbalance.

Formal modeling provides strong guarantees about system correctness, but developing and repairing formal models remains labor-intensive and requires substantial expertise in logic and formal reasoning. Recent LLM-based autoformalization agents seek to reduce this burden by generating candidate formal models and revising them using feedback from formal tools. However, the existing approaches follow a generate-and-repair paradigm, in which repairs are driven by verification failures of the generated model and therefore depend heavily on both the granularity of the feedback and the LLM's repair capability. As a consequence, a repair targeting one level of verification may invalidate properties at another level, which requires reasoning over the complete set of event guards. To address these limitations, we propose Proof-Sketch-Guided Formal Model Synthesis (ProGS), an autoformalization method centered on model-based proof sketches. A model-based proof sketch represents the proof structure of the target formal system as a tree. Internal nodes capture case splits and inductive reasoning steps, while leaf nodes correspond to concrete state-transition events that realize individual subgoals. ProGS uses LLMs to generate and repair these sketches, with verification failures mapped back to specific nodes and subtrees to provide structured guidance for iterative repair. Our evaluation on a benchmark of 27 formal systems shows that ProGS improves over state-of-the-art agentic formal modeling approaches in syntactic validity, deductive verifiability, and behavioral correctness, demonstrating the benefit of organizing formal model construction around hierarchical proof sketches.