Symmetric Structure and Motivic Transformation in Melodies, Phrases, and Themes
Alfredo González-Espinoza
AI 速览：作者用移位、倒影、逆行与循环移位生成的群，对852首键盘作品的旋律窗口做轨道与稳定子分析，量化旋律的动机词汇、部署与对称性。
Transposition, inversion, and retrograde are fundamental operations in music theory, from Schoenberg's twelve-tone technique to Forte's set classes and Lewin's transformational theory, yet their use in melodies has rarely been quantified. We read a melodic line through the orbits and stabilizers of its windows of $m = 3-6$ notes under the group generated by these operations and cyclic shift. The window entropy splits into an orbit entropy (motivic vocabulary) and a within-orbit entropy normalized by orbit size (deployment), and the group elements relating windows of one orbit give the motivic transformations. In 852 keyboard pieces spanning four centuries, at least 97% of melodies have lower orbit entropy than surrogates preserving their pitch content, spectrum, or one-step transitions ($m \geq 4$). Periods differ in vocabulary and symmetry types; musical forms differ in deployment. Recurring motifs are transposed 1.6 times more often than in random permutations of their forms, and transposed by a fifth or fourth 2.8 times more often, a preference that weakens from the Baroque to the 20th century and from Bach's fugues to Shostakovich's. Folk phrases and instrumental themes are rarely symmetric (2-10%), but are 1.6-5 times more often symmetric than note rearrangements. The framework extends to any symbolic sequence with a symmetry group.
We study coordinated groups of wallets on a bonding-curve launchpad (pump.fun on Solana), using a complete record of 200\,443 token launches, 15\,854\,121 curve trades and 51\,025\,958 SOL transfers over 88.3 hours. A prospective, multi-channel discovery procedure (co-buying, shared funding, joint signing, transfers, consolidation) yields 23\,710 wallet groups. Without ground-truth labels we validate them by out-of-sample link prediction, independent non-trading links and a comparison with naive co-buy clustering at equal numbers of flagged tokens: raw clustering collapses into one giant component, yet it ranks tokens at least as well as the groups, so the value of the structure is descriptive. Group activity is highly concentrated and splits into serial creators and long-lived rings of early buyers. Known members buy earlier than other buyers of the same token and extract more cash than an activity-matched placebo set, while late buyers' net cash flow is negative; tokens with members show a pump-like price path, but the contrast vanishes when controls are restricted to comparable tokens, so we report it as an association. A follower entering at the earliest group signal loses money out of sample in all 32 configurations and does no better than random entry. A few pools of tens to over a hundred fast wallets are associated with a two- to four-fold higher chance of reaching 20 SOL, also within creators, with a smaller excess at 60 SOL and none for graduation; on a final hold-out the team rules keep a precision of about one half to three quarters, yet many signals arrive when the curve already holds 20 SOL, one team supplies most of them, and they add no information beyond early curve state. We also document evaluation errors that turn the same data into apparent profit.
Changhao Li, Bradley A. Chase, Veena Vijayakumar, Mathys Rennela, Alessandro Cosentino, Naixu Guo, Sebastian Hassinger, Farrokh Labib 等 14 位作者
Quantum open-source software provides essential infrastructure for quantum science, and artificial intelligence (AI) is reshaping its capabilities and transforming its development. However, verifying quantum software at scale remains difficult, and AI-generated contributions can increase the workload of maintainers. In this Perspective, we examine verification as a central requirement for reliable AI-assisted quantum software development and research. We analyze public repositories, records covering 110 repositories from five annual quantum open-source hackathons that we organize, and responses from more than 1600 participants in a community survey. Our analysis connects limitations in automated verification with the review burden on quantum software maintainers. We propose verification practices and contribution standards that require contributors to support their changes with reproducible evidence for maintainer review. We also examine how quantum open-source software can provide infrastructure for AI-driven research whose results the community can independently verify and build upon. We maintain an open-source companion repository to support reproducibility and help projects adopt and refine these proposals. Together, these contributions help the quantum open-source software community translate advances in AI into reliable quantum research through reproducible verification.
Modern science has moved decisively toward larger and more collaborative research teams. Yet an influential 2019 study reported that small teams are more disruptive than large teams, a conclusion difficult to reconcile with both the well-known trend toward increasing collaboration and the disproportionately large teams behind widely recognized disruptive research, such as work that has been awarded Nobel Prizes. Here we show that the reported disruptive advantage of small teams is largely an artifact of measurement rather than a fact about teams. Analyzing about 60 million scientific publications, we find that larger teams cite more references and that the standard disruption index declines mechanically as reference lists lengthen. Equalizing reference-count distributions across team sizes reverses the negative gradient within the index's own framework. Evaluating each paper against one reference at a time yields a reference-robust measure that distinguishes recognized breakthroughs from ordinary papers more sharply and more consistently than the standard disruption index across six independently curated benchmarks, including the Nobel Prize. Under this validated measurement, scientific disruption increases with team size across four scientific domains and in every decade from the 1970s to the 2010s. For scientific publications, we conclude that larger teams are more, not less, disruptive.
How far can behaviour inside a group, and the group's performance, be predicted from members measured while alone? We tested this on three public datasets of human collective foraging (621, 128 and 1,133 participants). A low-dimensional individual representation estimated from private-phase movement was mapped onto behaviour inside the group through a mapping learned on other participants. Private information processing was stable between the two halves of a session (split-half reliability, the correlation between the halves, 0.60--0.83) and predicted behaviour inside the group with correlations of 0.30--0.66. Selective social learning, following those who have succeeded or stopped, showed stable individual differences inside the group (reliability 0.45--0.59) yet was not predicted at all from the same person's private behaviour. Group performance was predicted with a correlation of 0.55 in all three datasets by simulations never fitted to group outcomes or by the mean of individually measured performance, a prediction carried by mobility and individual performance rather than by social weights. We found no credible evidence for an effect of how members were combined (equivalence bound 0.06). Whom to follow thus emerges only in company, which delimits what solitary measurements can predict and compose.