Papers

The main purpose of this paper is to define and study the notion of restricted Rota-Baxter operator on restricted Lie algebras and restricted Lie triple systems. We provide the relevant properties and the usual connections with pre-Lie structures. We show that the operad of pre-Lie triple systems is the splitting of the operad of Lie triple systems. Moreover, we prove that Jacobson identities hold in pre-Lie triple systems in positive characteristic and then introduce the notion of restricted pre-Lie triple system.

How a growing tissue organizes its own homeostatic state is a central question in the physics of living matter. We show that when a growing epithelial sheet counteracts increasing cell density by mechanically squeezing cells out of its plane, a homeostatic in-plane pressure emerges as a generalization of a yield stress. We find that in the quasistatic growth limit the homeostatic state is marginally stable, with a pseudogap in the distribution of local distances to the extrusion threshold pressure. Because such mechanically induced extrusions arise from an instability of individual cells, the pseudogap is imprinted in the distribution of cell areas. This provides an image-based way to test for presence of mechanically induced extrusions and we identify this signature in the developing wing epithelium of D.~melanogaster. We expect the same principles to apply to confined three-dimensional tissues.

This paper proposes a new small area estimation approach that integrates Partial Least Squares within the Fay-Herriot model to address the challenges posed by high-dimensional and highly correlated auxiliary variables sets. The resulting Partial Fay-Herriot (PFH) estimator constructs supervised components that maximize their association with the target variable, enhancing model stability and predictive efficiency. Monte Carlo simulations demonstrate that PFH estimator achieves lower mean squared error than the standard Fay-Herriot estimator and outperforms principal components-based alternatives while relying on fewer latent dimensions. The methodology is applied to the estimation of district-level per capita consumption in Mozambique, where the survey data source is complemented by large set of correlated census variables. The resulting estimates highlight pronounced geographic heterogeneity and uncover spatial clusters of deprivation. Overall, the findings show that the proposed supervised dimension-reduction approach represents an effective and easily interpretable tool for producing reliable indicators in high-dimensional contexts.

Best match graphs (BMGs) were introduced in mathematical phylogenetics to describe the concept of closest relatives for related genes (leaves of rooted tree) in different organisms (defining leaf colors). We generalize this concept here to leaf-colored rooted networks, where least common ancestors are in general neither unique nor comparable. We characterize BMGs of rooted networks as those vertex-colored digraphs that are properly colored and satisfy an easy-to-check condition that we call the sicor-in-hub property. BMGs can be recognized in linear time and an explaining network can be constructed in quadratic time. Analogous results are obtained for reciprocal best match graphs (RBMGs), where an edge $\{x,y\}$ corresponds to pairs of vertices with different color that are mutually closest relatives.

The start of the Legacy Survey of Space and Time marks a new era for strong lensing science, where the number of strong lenses identified is expected to increase to $\mathcal{O}(10^5)$. In this paper we use a neural network to determine the precision with which lens parameters can be determined, using realistic simulated LSST lensed systems. We find that the Einstein radius can be measured with a mean precision of $3.7\%$ with calibrated uncertainties accurately reflecting the corresponding measurement error. Based on the performance of current strong lens classifiers, the $\sim 100,000$ detectable strong lenses are expected to be accompanied by a similar or larger number of false positives (non-lenses). In readiness for this we introduce a formalism, termed `COSMIC-BEAMS', to infer cosmological parameters while accounting for contamination by false positives. As a proof-of-concept, using simulated LSST measurements of the Einstein radii of a realistic and impure sample of photometric lens systems, i.e. those without spectroscopic confirmation, we find that the cosmological parameters $\Omega_m$, $\Omega_\Lambda$, and $w$ can be measured to a precision of $0.1$, $0.03$ and $0.15$ respectively for a $w$CDM cosmology. We demonstrate that unbiased cosmological parameters can be inferred even in strong lens samples contaminated by $50\%$ false positives, and that the photometric dataset of $100\,000$ strong lenses will provide equivalent $w$-precision to $2500-3500$ spectroscopic systems.

Deep learning segmentation of renal tumors requires large annotated datasets, yet clinical deployments typically offer only a handful of tumor-positive cases from the target site. We propose a diffusion-based inpainting framework that synthesizes anatomically plausible renal tumors within healthy CT scans, requiring no additional annotation, and provide the first systematic comparison of 2D, 2.5D, and full 3D (MAISI) synthesis strategies for this task. Training the diffusion model on public data (KiTS23, KIRC) and evaluating nnU-Net segmentation on a internal cohort across three low-data regimes, we find that 2.5D and 3D augmentation substantially reduce false positives (from $\sim$18–20% to $\sim$3–6%) while maintaining Dice, whereas 2D provides no consistent benefit. Crucially, the proposed 2.5D method matches full 3D synthesis on every metric at substantially lower computational cost, indicating that local volumetric consistency alone is sufficient for effective augmentation in data- and resource-scarce clinical settings.

Approximate high-level synthesis (HLS) and approximate logic synthesis (ALS) are two techniques for generating approximate circuits. They operate at different granularities. Approximate HLS typically modifies instructions in a control and data flow graph, whereas ALS modifies gates and interconnects in a gate-level netlist. The absence of a unified framework combining these techniques limits the potential for joint optimization. To bridge this gap, we propose to integrate ALS into the flow of approximate HLS. This integration expands the design space of approximate HLS by introducing fine-grained approximation induced by ALS, thereby generating approximate circuits with higher quality. Experimental results show that under the same error bound, our method reduces the hardware cost by 11% on average compared to the state-of-the-art methods.

Motivated by applications in fairness and foundational questions, we consider the problem of maximizing a monotone submodular function $f\colon 2^E \rightarrow \mathbb{R}_+$ over maximum cardinality sets in the intersection of two matroids on a common ground set $E$. An important special case is submodular perfect matching in bipartite graphs. Prior to this work, its approximability was poorly understood with only constant inapproximability known, despite not even a $\frac{1}{o(\sqrt{|E|})}$-approximation being known. Even when allowing to violate the cardinality constraint slightly, only a bicriteria approximation with a significant loss in the objective was known. Here, we obtain two results. First, we show that, within constant factors, the problem is approximation-equivalent to Submodular Orienteering in directed graphs. This yields an $\Omega(1 / \log |E|)$-approximation in quasi-polynomial time together with an almost-matching hardness result. Second, we obtain an improved polynomial-time bicriteria approximation via a local search framework. More precisely, if $f(T^*)$ is the largest submodular value of a common independent set in both matroids of size at least $K$, we find a common independent set $T$ such that $|T| \geq (1 - \epsilon) K$ and $f(T) \geq (1/2 - \epsilon) f(T^*)$. In contrast, previous work only guarantees a value of $\Omega(\epsilon) f(T^*)$ while ensuring that $|T| \geq (1 - \epsilon) K$.

Let $S$ be a free profinite group on a finite ordered basis $X$, and let $S^{(n,p)}$, $n=1,2,\ldots,$ denote its lower $p$-central filtration. There is a natural duality between $S^{(n,p)}/S^{(n+1,p)}$ and $H^2(S/S^{(n,p)},\mathbb{F}_p)$. These $\mathbb{F}_p$-linear spaces admit natural bases indexed by Lyndon words of length $\leq n$ in the alphabet $X$. These bases are known to be unitriangularly dual. We prove that they are much closer to being fully dual, by showing that the pairing between two basis elements vanishes unless the corresponding Lyndon words are permutations of one another. We further show that the value of the pairing is essentially independent of $n$.

Context: We developed a probabilistic machine learning method with the aim of performing the O(10)-way classification of low- and high-resolution spectra of stellar and extragalactic targets for the upcoming 4MOST survey. In fulfilment of the survey requirements, this method should be able to express uncertainty in the input data as well as uncertainty introduced in its prediction. Aims: Four different methods are explored: (1) convolutional neural networks (CNNs), (2) the Dirichlet distribution, (3) Monte Carlo dropout (MCD), (4) Bayesian neural Networks (BNNs) + variational inference (VI). Training and validation was performed using labelled spectra from the SDSS database and a custom 4MOST mock dataset. All the methods were compared in terms of the same metrics: accuracy, area under the curve (AUC), expected calibration error (ECE), Shannon entropy, negative log-likelihood (NLL), Brier score, training time, and inference time. Methods: A CNN with simple architecture and about 20,000 parameters was trained to achieve classification accuracies of 91.5% on SDSS data and 92.8% on 4MOST mock data. The direct Dirichlet prediction and VI models tested provide uncertainties on class membership probabilities, but they confuse classes more often. The MCD on a CNN is found to be the most suitable; it boosts the point-estimate accuracies to 92.6% and 93.9%, while still providing fast training and sufficiently fast inference. Compared to a standard CNN, the method additionally provides well-calibrated uncertainties at marginal extra cost.

Equivalent finite parameterizations can represent the same functions and intrinsic norm yet induce different optimization algorithms. We study this effect in a controlled finite Brownian RKHS with nodal, increment, and spectral coordinates. Classical finite-element, RKHS-interpolation, Brownian-covariance, and mixed-boundary DCT identities make the shared hypothesis class, Brownian energy, approximation operator, and coordinate maps explicit. Our main results concern the optimization geometry of this fixed model. With mapped initialization, identical scalar steps, and identical minibatches, nodal and spectral GD/SGD have exactly the same mapped trajectories. Increment GD is an explicit Euler step for the constant Brownian/Sobolev metric, with factor $1/h$. For Brownian-regularized least squares, $\kappa_2(\mathbf H_{\mathrm{inc}})\le1+A/\rho$, independently of grid resolution $G$ for fixed $A$, $\rho>0$, and the stated normalization. Under the stated standard-Adam convention, the universal orthogonal equivariance group is exactly the signed permutations; the block DCT-VIII transform is not one. Float64 tests over five grids numerically verify the finite identities, mapped one-layer and recursive trajectories, conditioning predictions, and theorem-matched Adam separation. Thus coordinate effects are isolated without changing the represented functions, intrinsic regularizer, or approximation space.

We provide kernel estimates for pseudo-differential operators in the $S(m,g)$ Weyl-Hörmander calculus classes. These new results lead to boundedness theorems like the weak (1,1) type for these classes and the boundedness of these operators from Hardy spaces to Lebesgue spaces $L^p$. We prove that under a suitable hypoelliticity condition on the weigh $m,$ one can get the weak (1,1) inequality for the Fefferman order established previously by the second author in analogy to the classical $L^p$-boundedness theorem due to Fefferman. Our approach makes an extension to $S(m,g)$ classes of previous estimates proved by Álvarez and Hounie, Nagase, Kumano-Go, etc, for the Hörmander classes including new regularity properties in this framework from the Hardy space $H^p$ to $L^p$ and also on Lorentz spaces. We have identified that the Uniform Hörmander Condition plays a fundamental role in some of our boundedness theorems.

In this paper, we provide a systematic construction of quantum modules associated with coadjoint orbits of asymptotic symmetry groups through the path integral quantization at one-loop order. In particular, for the orbits with Hamiltonians unbounded from below, we show that an appropriate choice of integration contour defines a convergent Euclidean half-line path integral. The reference state associate with the orbit is determined by the path integral of the geometric action on the corresponding coadjoint orbit. The coadjoint module is therefore spanned by the reference state and its descendants. We apply this formalism to the Virasoro and BMS$_3$ groups and derive the coadjoint modules corresponding to all constant orbits. We also compute the characters of all constant Virasoro and BMS$_3$ coadjoint orbits by counting the states within the modules, and the results agree with the corresponding computations from the path integral of the geometric action with a periodic Euclidean direction.

A robot can predict failure and still be unable to prevent it. By the time a safety mechanism reacts, the nominal plan may already have spent the control authority that recovery requires, and fixed task priorities may block whatever response remains. Our key insight is that both aspects are decided inside the controller. Recoverability must inform actions while they are chosen rather than veto them afterward, and task objectives must be adapted as recoverability shrinks. Building on this, we present RAYA, a hybrid learned-analytic framework that places a learned finite-horizon recoverability margin inside an optimal controller with hard constraints and pairs it with a bounded learned scheduler that shifts task weights to facilitate recovery. Across 7,200 simulation episodes per controller spanning quadrotor and autonomous-vehicle benchmarks, RAYA not only improves survival rates, but also transfers the learned components zero-shot to unseen trajectories, disturbances, plant shifts, and friction layouts. We developed an embedded realization of RAYA and deployed it on-board a 35g Crazyflie quadrotor. Across 40 combined hardware flights under wind with either aerodynamic mismatch or an unmodeled 40% motor-command loss, each of three baselines fails in all trials, while RAYA completes 10/10 six-cycle missions. Project Website: https://raya-control.github.io/.

Uniform distribution modulo 1 is a classical notion of pseudo-randomness for sequences in the unit interval, which is quantified in terms of the discrepancy. Sequences whose discrepancy is of the smallest possible asymptotic order are called low-discrepancy sequences. The Poissonian pair correlation is another notion of pseudo-randomness, which studies the distribution of the gaps between pairs of elements of the sequence on a local scale. It is known that Poissonian pair correlation implies uniform distribution mod 1, and that the opposite implication is not true in general. It has also been observed that classical examples of low-discrepancy sequences fail to have Poissonian pair correlation, and it has been speculated that the two properties might be irreconcilable due to the high degree of structural rigidity that is required for low-discrepancy behavior. As we prove in this paper, this is not the case: we construct an example of a low-discrepancy sequence with Poissonian pair correlation.

We study random signed Takagi–Landsberg bridges with independent Rademacher Faber–Schauder coefficients. At index $H=1/2$, we prove that every fixed deterministic refining sequence of partitions with vanishing mesh yields quadratic variation $t$, almost surely and uniformly in $t\in[0,1]$. For partitions that need not be refining, the mesh condition $o(1/\log n)$ is sufficient, and its order is sharp. Our proofs use an operator representation of the quadratic sums and moment bounds for Rademacher chaos. We also show that asymmetric signs can destroy this invariance. At every index $H\ne1/2$, we construct a deterministic refining sequence along which the critical $p$-power sums, with $p=1/H$, have two distinct finite accumulation points almost surely. At $H=1/4$, uniform thirds grids provide an explicit alternative to the dyadic limit. Thus $H=1/2$ is the unique index in the symmetric family at which critical variation is invariant along every fixed deterministic refining sequence. Nevertheless the variation index equals $1/H$ almost surely across a large sequence of partitions.

Let $\mathcal K$ be the convex hull of a planar Brownian motion up to time $1$. We explicitly determine the probability that $\mathcal K$ contains a prescribed point $z\in\mathbb R^2$. The proof is based on a general formula relating the radial function of a random convex body to its support function and its derivative, together with a comparison of $\mathcal K$ with an arcsine-rescaled Gaussian ellipse. We also obtain an analogous formula for the convex hull of a planar Brownian bridge. Finally, we derive small- and large-time asymptotics for the corresponding coverage probabilities.

Privacy leakage in LLM agents is commonly evaluated within individual components such as memory, retrieval, or tool-use pipelines, which makes it difficult to distinguish internal exposure from information that an external observer can actually recover. We present CIPL (Channel Inversion for Privacy Leakage), a channel-aware evaluation framework for black-box privacy leakage in LLM agents. CIPL represents a target through sensitive source, selection, assembly, execution, observation, and extraction stages and evaluates the transition from selected sensitive units to attacker-recoverable output under a shared protocol. Experiments across memory-based, retrieval-mediated, and tool-mediated targets, together with a BrowserUse live-agent case study, show that storage labels alone do not determine recoverability. Memory targets form a near-saturated reference case, retrieval-mediated leakage is frequently partial, and tool-mediated and live-agent leakage varies strongly with observation surface, prompt-to-channel alignment, retrieval depth, and provider behavior. A stratified semantic audit further identifies attacker-useful disclosures that canonical exact matching misses. CIPL therefore provides a common framework for comparing how internal sensitive dependence is realized as externally recoverable leakage across heterogeneous agent pipelines.

We study the first exit of an isotropic planar Ornstein-Uhlenbeck process from an annular sector, the region bounded by two concentric circular arcs and two radial segments, and obtain explicit eigenfunction expansions for the associated exit functionals. After the ground-state transformation that renders the generator self-adjoint, polar separation reduces the problem to a radial confluent hypergeometric equation whose two independent (Whittaker) solutions of generally non-integral order are combined through a two-radius determinant that fixes the spectrum. In this way we obtain the survival probability, the density and moments of the exit time, and -the principal contribution -the joint law of the exit time and the exit boundary, which resolves both the instant of exit and the boundary piece through which it occurs. As a companion separable case, we also treat a genuinely correlated, reversible planar Ornstein-Uhlenbeck process on a principal-axis rectangle, where the radial functions are replaced by parabolic cylinder functions: the survival probability factorizes into one-dimensional problems, while the joint law of the exit time and the exit side does not. The expansions require only one-dimensional root-finding and quadrature and are validated against Monte Carlo simulation. An application to an optically trapped colloidal particle is discussed, a setting in which the annular geometry arises naturally.

We study a representative-agent Epstein-Zin economy with geometric dividends and a hidden finite-state Markov drift. We allow the price-dividend ratio to contain an additional positive, absolutely continuous valuation factor and, within the class $\mathfrak C$ defined below and under the regularity, admissibility, and positivity conditions of our main theorem, equilibrium forces this factor to be constant, yielding belief-Markovian prices. In the two-state case, under the stated positivity condition and strictly positive transition intensities, we prove existence, uniqueness, endpoint smoothness, interior analyticity, and uniform bounds for the positive solution of the pricing equation. For $0<\theta\leq1$, this solution supports an equilibrium under any continuous short rate satisfying the model's one-sided portfolio condition. Finally, in the two-state subregion $\eta>0$, we derive belief-dependent stock volatility, a European option-pricing PDE, and a leading short-maturity conditional risk-neutral log-return skewness expansion.

Conversational speech depends on dialogue context and the listener's immediately preceding behavior. We propose ReACT-TTS, a two-stage framework that uses a one-second pre-response listener facial sequence to plan the next utterance's emotion and prosody before speech realization. On a strict dyadic MELD protocol, Temporal conditioning yields higher mean macro-F1 and VAD concordance than Text-only across ten seeds, while accuracy remains essentially unchanged. Ablations show that temporal modeling performs best among the visual variants and that an explicit early-to-late difference is unnecessary; correct listener reactions also outperform cyclic mismatches on average. In a contextual-appropriateness study with 20 speech researchers, 76% of judgments prefer Temporal, 9% Text-only, and 15% report no preference. We further connect the predicted response style to a Grad-TTS backbone for end-to-end speech realization. Overall, the results support pre-response listener dynamics as complementary cues for conversational response planning. The source code is available at https://github.com/CYJ1/ReACT-TTS_public.

Let $G$ be a simple graph of even order at least four, and let $K_G$ denote the complete graph on $V(G)$. A perfect matching of $K_G$ is called a pairing of $G$. The graph $G$ has the Pairing-Hamiltonian property, or PH-property, if every pairing $M$ of $G$ admits a perfect matching $N\subseteq E(G)$, disjoint from $M$, such that $M\cup N$ is a Hamiltonian cycle of $K_G$. We prove that the PH-property is preserved under Cartesian products. More precisely, for graphs $G$ and $H$ of even order at least four, we show that both $G$ and $H$ are PH if and only if every pairing of $G\square H$ admits a Hamiltonian completion contained in a spanning union of vertex-disjoint prisms determined by a perfect matching of $G$ or of $H$. Without this support restriction, the converse fails: a Cartesian product may be PH even when neither of the two graphs is PH.

We study performance portability for low-order, matrix-free finite element kernels, using the example of a vectorial, variable-coefficient PDE operator originating in geophysical models. Written in Kokkos, the kernel is compared on NVIDIA H100, AMD MI250X, AMD MI300A and Intel PVC Max 1550 GPUs. Owing to its low order and to optimizations that reduce the arithmetic, the kernel has a low arithmetic intensity, so that its performance is determined by how the finite element assembly is mapped onto the memory hierarchy. This is a dimension in which the architectures differ even within one vendor family, causing different performance characteristics. We examine how Kokkos' hierarchical parallelism and shared scratch memory, which are used for the shared degrees of freedom of the conforming discretization, behave on each device. Finally, we show how portability gaps can be narrowed with tuning levers such as the size of the thread groups, the balance between occupancy and register use, and the atomic accumulation strategy at the end of the kernel.

We prove that every bounded stable entire solution $v$ of the Allen–Cahn equation in $\R^3$ is one-dimensional. As a consequence, the full De Giorgi conjecture in $\mathbb{R}^4$ is true. We also obtain local curvature estimates for stable solutions. The proof strategy is inspired by the recent breakthrough work of Chan, Fernández-Real, Figalli and Serra [J. Amer. Math. Soc. 2026], by reducing the stabilty condition for the Allen-Cahn equation to a weak stability condition on a surface (the zero set) and then utilizing Gauss-Bonnet formula. For this purpose, we first use the stability condition to get a sublinear bound for a weighted integral that controls the zeros where the solution is far from planar. If such zeros exist, we isolate a bounded set of them and join $1-v^2$ near this set to derivatives of one-dimensional transitions farther away. By controlling the interaction between these transitions, we derive the weak stability condition on the zero set, which is then used to bound a weighted integral of the squared curvature on the regular part of the zero set by a cutoff gradient integral and a controlled error. We use this inequality to bound the intrinsic area and construct logarithmic cutoffs. The resulting compactly supported test function has a negative contribution near this set that exceeds all joining and cutoff errors, contradicting stability.

We determine the full automorphism group of every connected Cayley graph on an almost simple group with a normal connection set. We also characterize exactly when the full automorphism group is generated by right translations, group automorphisms preserving the connection set, and inversion. Our results substantially generalize several results in the literature, including the known determinations of the automorphism groups of derangement graphs, complete transposition graphs and complete alternating group graphs. As a further application, we establish criteria for a finite nonabelian simple group to admit a graphical doubly regular representation and determine exactly which alternating groups do so, correcting claims in the literature.

This study examines phosgene (COCl2) adsorption on pristine and noble metal-doped (Ag, Au, Pd, Pt) B12N12 nanocages using dispersion-corrected density functional theory [B3LYP-D3(BJ)]. Boron-site substitution narrows the HOMO-LUMO gap far more than nitrogen-site substitution (69-82% vs 41-67%) and was adopted throughout. All systems were fully optimized; multiple starting geometries converged to two stable minima per dopant, X-O and X-Cl. Pristine B12N12 binds phosgene weakly (Eads = -12.8 to -24.9 kJ mol^-1). Doping strengthens binding, spanning -14.0 to -60.7 kJ mol^-1 after counterpoise correction, with platinum exhibiting the highest affinity and structural stability. Natural population analysis indicates phosgene donates at most 0.33 e, and QTAIM classifies all cage-adsorbate bond critical points as closed-shell or intermediate, confirming physisorption. Vibrational frequency analysis confirms all structures as true minima and reveals that the adsorption entropy penalty (59-161 J mol^-1 K^-1) is decisive. Under Grimme's quasi-harmonic approximation, pristine cages fail to bind phosgene (Delta G = +23.8 to +27.9 kJ mol^-1), whereas only Pt-O (Delta G = -8.8 kJ mol^-1) and Pd-O (-7.2 kJ mol^-1) adsorb phosgene spontaneously at 298 K. Transition-state theory indicates rapid room-temperature recovery (tau = 43 ms for Pt-O), while thermodynamic desorption occurs at 69.6 deg C, ensuring a practical regeneration window. Silver-doped cages provide narrow post-adsorption gaps and high electrophilicity but cannot retain phosgene at ambient conditions. Platinum doping is therefore the most effective strategy for reversible phosgene detection using B12N12 nanocages.

Recent advances in large reasoning models (LRMs) have made machine unlearning more challenging, as protected facts or unsafe rationales may surface in intermediate chain-of-thought (CoT) traces before the final answer is produced. Existing unlearning objectives typically suppress the target content or redirect internal representations, but they never specify how the post-forgetting trajectory should continue, which can lead to hallucinated substitutes, malformed boundaries, or repetitive outputs. We argue that LRM unlearning should instead learn a natural forgetting trajectory: a coherent non-disclosing CoT followed by a stable refusal-style answer that replace the original disclosure. To this end, we propose Guided Answer-Reasoning Distillation (GUARD), which converts model-generated unsafe disclosures into safe-exit trajectories, aligns a frozen LRM via guidance tokens, and distills the guided behavior into model parameters. To address the lack of metrics for replacement quality beyond leakage, we further introduce Natural Forgetting Reasoning Score (NFRS), which captures structural stability, fluency, and unsupported substitutes in forgotten outputs. Extensive experiments on R-TOFU and a STAR-1-derived harmful-intent setting show that GUARD substantially reduces unsafe and privacy disclosures across two widely adopted distilled LRMs while preserving reasoning utility.

We present the Spoken Wikipedia Presentation Corpus, an extension of the Spoken Wikipedia Corpora featuring LLM-generated slide decks for multimodal ASR. Slides are created from LLM-segmented sections using a hybrid pipeline that combines LLM-based content planning with rule-based design decisions. For each section, an LLM generates a slide title, bullet points, a takeaway message, and a visual description that is used to create an illustration. Rule-based matching then selects layouts, themes, and styles to produce the final slides. A vision LLM extracts slide text as Markdown. We evaluate multiple ASR and spoken language models (SLMs). The best model achieves an average micro-WER of 10.23% and an average micro-CER of 6.48% on audio-only inputs. English yields the lowest error rates, followed by German and Dutch, while performance declines across lower-resource languages. Although audio-only baselines are strong, multimodal zero-shot prompting of omni models remains challenging. The aligned slide, text, and audio data show a strong potential to improve recognition through cross-modal context.

Despite the remarkable progress in Multimodal Large Language Models (MLLMs), prevailing Chain-of-Thought (CoT) paradigms remain confined to the natural-language expression space. Consequently, they inherently incur excessive linguistic overhead, leading to information dilution and weak visual grounding. To address this challenge, we propose Dense Reasoning Trace (DRT), a paradigm that departs from natural-language-centered CoT by expressing reasoning as compact structured traces, which include concise intermediate states with symbolic connectors and disentangle visual observations from logical deductions. First, we introduce the Dense Trace Initialization to internalize the DRT reasoning mode into the model, substantially improving token efficiency while preserving visual evidence. To further enable the model to faithfully capture the logical relations within traces, we propose the Trace-Grounded Reinforcement Learning framework, which builds reference traces through a tri-perspective verification pipeline and employs Trace-Grounded GRPO with structured rewards, encouraging the model to generate concise DRT-style traces with reduced hallucination and stronger logical grounding. Extensive experiments on challenging reasoning benchmarks show that DRT achieves 5.5$\times$ token efficiency improvement while improving 1.3 accuracy points over the Qwen3-VL baseline. These findings suggest that complex multimodal reasoning may not require verbose natural-language traces, opening a more efficient path for next-generation MLLMs. Our code and data are available at: https://github.com/HIT-leaderone/DRT

The pre-season strengths of European football clubs are usually measured by two proxies in the literature. Football Club Elo Ratings provide strictly performance-based Elo ratings from the early days of the European Cups, while Transfermarkt valuations are crowd-based estimates of squad market values. This paper compares them by evaluating their ability to forecast the results of matches played in the UEFA Champions League and the UEFA Europa League between the seasons 2020/21 and 2024/25. The two indicators yield almost identical out-of-sample accuracy when used separately. Combining the two measures leads to a modest improvement, but the best aggregation procedure is sensitive to the forecast target. Our results suggest that seeding based on Elo ratings would be (closely) optimal.