To live meaningfully, we can’t just be receptacles for the right sorts of activities – it has to matter that it’s us living our lives. Something is missing in valuable activities, if the same value could be achieved by anyone who performs the task. Meaningfulness requires that it be our own ideals, personalities, and priorities contributing to the value of what we do. Recognizing this can shed light on our relationship with meaning in three ways. First, it shows a distinctive reason that autonomy is important: what we do without autonomy will lack meaning. Second, it helps us understand a challenge we encounter when facing trade-offs between different types of meaning, navigating between opportunities to have a few of our characteristics matter widely (e.g., as a filmmaker or an activist) and intimate contexts in which much more of who we are matters to a small group of people. Finally, if living meaningfully involves our central characteristics shaping what’s valuable about our actions, then discovering pre-set purposes (e.g., from fate, God, or the cosmos) might actually undermine our capacity to live meaningful lives.

This study presents a comprehensive analysis of the frequency response characteristics in a gas generator cycle liquid rocket engine, employing modular decomposition and linearised frequency-domain modeling to simulate dynamic behaviours under forced oscillations. The engine is dissected into key subsystems, including liquid pipelines, turbopump assembly, valves, flow regulation components, thrust chamber, gas generator and pyrotechnic starter, highlighting features such as centrifugal pump pressurisation, staged combustion and cavitation mitigation via venturis. Three oscillation scenarios are examined: supply system responses to thrust chamber pressure disturbances, combustion component responses to fluid disturbances and combustion component responses to pump speed disturbances. Simulations over 0–2000 Hz reveal acoustic-dominated traits in the thrust chamber with oxidiser pathway dominance, low-frequency emphasis in the gas generator driven by fuel disturbances, and heightened instability risks from pump pulsations. Parametric analyses demonstrate that increased pipeline lengths shift resonant frequencies downward, elevated injector pressure drops enhance stability margins by 1.6% with a 20% pressure drop increase, and chamber structural/gas parameter variations erode system stability. These insights, validated against benchmark models, inform strategies for mitigating combustion instability, optimising design parameters, and improving reliability in high-thrust propulsion applications.

This article proposes a topic modeling method that scales linearly to billions of documents. We make three core contributions: i) we present a topic modeling method, tensor latent Dirichlet allocation, that has identifiable and recoverable parameter guarantees and sample complexity guarantees for large data; ii) we show that this method is computationally and memory efficient (achieving speeds over 3$\times $–4$\times $ those of prior parallelized latent Dirichlet allocation methods), and that it scales linearly to text datasets with over a billion documents; and iii) we provide an open-source, GPU-based implementation of this method. This scaling enables previously prohibitive analyses, and we perform two real-world, large-scale new studies of interest to political scientists: we provide the first thorough analysis of the evolution of the #MeToo movement through the lens of over two years of Twitter conversation and a detailed study of social media conversations about election fraud in the 2020 presidential election. Thus, this method provides social scientists with the ability to study very large corpora at scale and to answer important theoretically-relevant questions about salient issues in near real-time.

The Ghana–Togo border separates the Ewe people from their ritual spaces and objects. In Nyive, a border town divided into Ghana Nyive and Togo Nyive, these ritual spaces and objects are in Togo Nyive. The liminal space of the border complicates ritual practice by preventing community members from moving the ritual drum Aɖaʋatram (madness has led me astray) across the river and the international border. Nonetheless, communities in Nyive use ritual archives to maintain their identities in the context of colonial separation. They remake their identities through the symbolism, origin narrative, handling, and use of the drum Aɖaʋatram.

We give a new proof of the singular continuity of Minkowski’s $?$-function. Our proof follows by showing that the maximal Lyapunov exponent of a specific pair of $3\times 3$ nonnegative integer matrices related to Stern’s diatomic sequence is strictly greater than $\log 2$.

Silvennoinen (2025) analyzes the stored sequence going forward as an adverb that inherits adverb-class morphosyntax. This reply challenges that categorization on empirical grounds. The construction fails the key distributional test for adverbs: it cannot occur in integrated-medial position between subject and verb (*We going forward will prioritize replication), the diagnostic slot for core adverbs (We certainly will prioritize replication). Analysis of Silvennoinen’s corpus (n = 1,517) confirms this restriction – apparent ‘medial’ tokens prove either to be NP-internal modifiers or parenthetical supplements, never integrated clausal constituents. Instead, going forward patterns with PP adjuncts, occurring clause-initially, clause-finally, or as supplements. Internally, deverbal going heads the construction and licenses a directional complement forward(s), parallel to established deverbal prepositions like according [to …] and depending [on …]. The construction thus projects PP, not AdvP, aligning with The Cambridge Grammar of the English Language’s flexible-complement analysis of prepositions. This case demonstrates that storage and semantic specialization do not force categorical reanalysis.