Text-to-image diffusion models have achieved impressive results in synthesizing high-quality images from natural language prompts. However, commonly used prompting strategies remain relatively generic, limiting the model's ability to accurately express emotional intent and nuanced affective attributes. This work proposes EPIG, a method that enhances emotional expressiveness at the prompt level prior to image generation. Grounded in psychologically informed emotion representations (valence-arousal) and leveraging structured, role-aware prompt enrichment, EPIG enriches emotion-related components of prompts without modifying or retraining the image generation backbone. The resulting emotion-aware prompts guide the generative process toward more emotionally coherent visual outputs, with particular effectiveness in controlling arousal. EPIG is lightweight, training-free, and well suited for resource-constrained and personalized image generation scenarios. Experimental results on a benchmark of 10 diverse prompts show that EPIG reduces mean arousal error compared to strong baselines, including naive insertion and LLM-based prompt expansion, with reductions of 14% and 12%, respectively. These improvements are statistically significant. EPIG also preserves valence alignment and semantic consistency, as measured by CLIPScore and supported by ablation studies. The effect is more pronounced on prompts containing explicit subjects such as humans, children, or animals, where the reduction reaches 17%, highlighting the subject-sensitive behavior of the proposed method.

Machine-learning drug-discovery pipelines increasingly rely on generative models that propose molecules far from the data used to train downstream synthesizability filters. Existing filters (SAScore, SCScore, RAscore, DeepSA) are purely statistical and degrade in exactly this out-of-distribution (OOD) regime. We ask whether cheap, closed-form physical priors, used as auxiliary supervision on a graph neural network (GNN), improve OOD generalization. We add two auxiliary losses to a GINE backbone: a topological complexity regression supervised by the Bertz index, and a strain-energy soft penalty supervised by MMFF94 force-field energy. On a 65,177-molecule corpus (HIV, Tox21, COCONUT) labeled by SAScore thresholds we reproduce a strong in-distribution baseline, then evaluate a 4-way ablation (baseline / +complexity / +strain / +both) on a single-source OOD split (train on drug-like HIV+Tox21, test on COCONUT natural products), repeated over 5 seeds with paired bootstrap confidence intervals. All three physics-aware variants give a small but statistically significant OOD improvement over the baseline (mean OOD AUC 0.9774): +complexity Delta = +0.0060 (95% CI [+0.0023, +0.0102]), +strain Delta = +0.0032 ([+0.0008, +0.0052]), +both Delta = +0.0066 ([+0.0038, +0.0093]); every interval excludes zero, and the combination is best. The variants are indistinguishable in-distribution, so the effect is visible only under OOD evaluation. We are explicit that the effects are modest, and we report a cautionary methodological finding: a single-seed version of this experiment produced a qualitatively different (non-monotone) story that did not survive multi-seed evaluation.

The discovery of novel superconducting materials is a longstanding challenge in materials science, with a wealth of potential for applications in energy, transportation, and computing. Recent advances in artificial intelligence (AI) have enabled expediting the search for new materials by efficiently utilizing vast materials databases. In this study, we developed an approach based on deep learning (DL) to predict new superconducting materials. We have synthesized a compound derived from our DL network and confirmed its superconducting properties in agreement with our prediction. Our approach is also compared to previous work based on random forests (RFs). In particular, RFs require knowledge of the chemical properties of the compound, while our neural net inputs depend solely on the chemical composition. With the help of hints from our network, we discover a new ternary compound $\textrm{Mo}_{20} \textrm{Re}_{6} \textrm{Si}_{4}$, which becomes superconducting below 5.4 K. We further discuss the existing limitations and challenges associated with using AI to predict and, along with potential future research directions.

The 2022--2026 burst of activity in small-format matrix multiplication (AlphaTensor 2022, AlphaEvolve 2025, Schwartz--Zwecher 2025) has produced striking individual results but scattered them across different fields, attribution conventions, and serialisation formats. A complementary line of work -- Perminov's open-source flip-graph framework~\cite{perminov2026fast,perminov2025fast} -- instead drives existing construction methods, notably flip-graph and \emph{meta-flip-graph} search, at scale across large format spaces, discovering many new low-rank schemes (including ternary-integer ones) that further enrich the landscape this catalog must unify. We present a unified, machine-checkable catalog covering shapes up to \nmpshape{32}{32}{32} over \Rationals, \Integers, \Reals, \Complex, and \Ftwo, with a separate axis for commutative algorithms (Waksman 1970, Makarov 1986, Rosowski 2019). Derivation over this catalog is performed by a \emph{frontier-closure search} that recombines catalog entries by axis-flip, Kronecker, axis concatenation, serendipitous products, recombination-with-allocation (with optional output peeling and pair fusion), and downward projection. A central methodological point is the \emph{non-overlap property}: our recombination does not, and cannot, rediscover the shared bilinear products that hand-crafted constructions (Strassen, Laderman, Smirnov, AlphaTensor) are built around. This draws a clean line between the ``find a cleverer bilinear core'' and ``compose known cores'' axes of progress, and resolves several attribution puzzles in the literature. We refresh the DIS09 comparison tables, split per field and with a commutative column, and provide the tooling to regenerate them automatically as the catalog evolves.

Frobenius' theorem settles, definitively, the question of three-dimensional real division algebras: there are none. What it leaves open -- and what this paper addresses -- is the question of which three-dimensional real associative algebras actually exist. We call these \emph{near-trinions} and classify them completely, up to $\mathbb{R}$-algebra isomorphism. The answer is exactly six isomorphism classes; we provide canonical representatives, explicit multiplication tables, and a collection of module-theoretic invariants sufficient to distinguish every pair. The classification proceeds by stratifying on the radical dimension $d$: Wedderburn--Artin resolves the semisimple stratum; in the $d=1$ stratum, the Peirce decomposition locates the radical generator in either a diagonal or off-diagonal corner, producing the commutative and non-commutative branches respectively and ruling out the residue field $\mathbb{C}$ by a characteristic sign obstruction; and the $d=2$ stratum splits on whether Jac$(A)^2$ vanishes. The argument not only recovers the six classes but explains why the radical dimension takes values in $\{0,1,2\}$, why the $d=1$ case splits on commutativity, and why no near-trinion with residue field $\mathbb{C}$ can exist. One direction for subsequent work is proposed.