In 1985, Adams [‘The algebraic independence of certain Liouville continued fractions’, Proc. Amer. Math. Soc. 4 (1985), 512–516] proved that any finite number of Liouville series in different bases are algebraically independent. In this paper, we prove the equivalence between algebraic and linear independence when the bases are equal.

This research paper aimed to determine if bio-stimulation affects peri-oestrous behavioural patterns of buffalo heifers and can improve oestrous behavioural responses through fenceline and direct contact with bulls during the heifers’ first and second oestrous cycles. Buffalo heifers are known to have poor and less intense expression of oestrus behaviour. This leads to lower oestrous detection rates and ultimately results in poor reproductive efficiency. Providing social cues, such as bio-stimulation, is an effective technique for improving oestrous behaviours in cattle, pigs and sheep. For this study, 24 pre-pubertal Murrah heifers were allotted to 3 groups of 8 each; similar in age (15.08 ± 0.16 months) and body weight (199.5 ± 0.21 kg). In T0, heifers were not exposed to a bull; in T1, heifers had continuous exposure to a bull behind a fenceline; and in T2, heifers were directly exposed to a bull twice daily (6 hours total). Oestrous behaviours were recorded on days −3, −2 and −1 (prior to oestrus), day 0 (day of oestrus) and on days +1, +2 and +3 (post-oestrus) using 24-hour digital cameras. Oestrous behaviours (sniffing/licking, tail raising, micturition, chin resting and mounting attempts) commenced on day −3 or day −2, peaked on day 0 and waned by day +2 or day +1 during both oestrous cycles. Oestrous behaviour frequencies were higher for the heifers in T1 and T2 groups (P < 0.05) in comparison to the T0 group during both cycles. Receptive standing in response to mounting was only observed during the second oestrous cycle on the day of oestrus, and the frequency was significantly highest in T2, followed by T1 and T0 (P < 0.05). It was concluded that direct or fenceline bull exposure triggered more expression of oestrous behaviours in buffalo heifers, with direct exposure having a greater effect than fenceline exposure.

The Speaker of Parliament is potentially a highly influential actor in parliamentary politics. Yet, we know surprisingly little about how they make decisions. In many parliaments, they, for instance, choose who gets to speak in question time. By examining a unique data set from the Netherlands, which lists all proposed oral questions and which ones were selected to be asked in parliament, this paper examines the considerations of the Speaker when selecting questions. This gives a unique insight into their considerations in general. Our central question is as follows: under what conditions are Speakers more likely to select an oral question? We look at the following three options: the neutral arbiter that seeks to treat all parties fairly; the partisan Speaker who defends the interests of their own party; and the asset of the coalition that protects the unity of the governing coalition. Our analyses indicate that Speakers are more likely to block questions that would drive a wedge in the coalition and are more likely to accept questions that meet established norms of urgency and importance.

We present a detailed study of the evolution of the number of connected components in sub-critical multiplicative random graph processes. We consider a model where edges appear independently after an exponential time at a rate equal to the product of the sizes of the vertices. We provide an explicit expression for the fluid limit of the number of connected components normalized by its initial value, when the time is smaller than the inverse of the sum of the square of the initial vertex sizes. We also identify the diffusion limit of the rescaled fluctuations around the fluid limit. This is applied to several examples. In the particular setting of the Erdős–Rényi graph process, we give the fluid limit of the normalized number of connected components, and the diffusion limit of the scaled fluctuations in the sub-critical regime, where the mean degree is between zero and one.

This article argues that West Papuan independence activists reveal the limits of decolonisation as a universal project of self‑determination. It shows how sub‑state actors were squeezed between transnational anticolonial solidarities and an international order increasingly structured around nation‑states. Focusing on the 1960s, it traces how West Papuan leaders sought to turn a territorial dispute into a people‑centred claim to self‑determination by mobilising race‑based transnational networks that linked Melanesia to a wider Black International. Drawing on the personal papers of Nicholas Jouwe and West Papuan petitions to the United Nations and the Organisation of African Unity, the article reconstructs efforts to enlist African and Caribbean diplomats as advocates in debates over the New York Agreement and the 1969 Act of Free Choice. It shows that, while Papuan activists strategically racialised themselves as Black and Melanesian to articulate decolonisation’s unfinished business, Indonesian diplomats and many postcolonial states activated civilisational hierarchies and the discourse of development to deny their claims and close off alternative futures. By following Papuan actors across local, regional, and global arenas after formal empire, the article demonstrates how decolonisation’s discontents arose not only within new nation‑states but also from the international norms that purported to universalise self‑determination.

This article examines the construction of a continuous history of Iranian art and architecture in André Godard’s L’Art de l’Iran (The Art of Iran). Relying on the strategic use of periodization, Godard stages continuity as a narrative achievement, anchoring it in geography, displacing it during moments of foreign rule, concealing it beneath surface forms, and reactivating it under favorable conditions. Rather than treating historical periods as neutral divisions, this article shows how periodization operates as a historiographic strategy that stabilizes continuity by managing disruption, marginalizing rupture, and selectively rendering certain forms, regions, and temporalities visible while excluding others.

Southeast Asia’s coasts are among the world’s most physically and ecologically sensitive environments, facing escalating threats from climate change, rising seas, extreme events and pervasive land subsidence. Understanding the magnitude, rate and trajectories of coastal transformation is critical for adaptation planning and hazard mitigation. This review synthesises current knowledge of coastal landform change across Southeast Asia (SEA), emphasising spatial and temporal variability driven by geological, climatic and anthropogenic boundary conditions. While globally sea levels are rising, tectonic deformation and vertical land motion dominate local trajectories, resulting in large spatial variability in relative sea-level rise (RSLR), offsetting SLR in uplifting areas and amplifying it in subsiding areas, where rates exceed 8 mm/yr, rivalling those of the Holocene marine transgression and surpassing global averages. The evolution of coastal landform types in response to boundary controls is examined. Paleo-reconstructions reveal that the Holocene transgression inundated ~2.3 million km2 of the Sunda Shelf, fundamentally resetting the land–sea interface of SEA countries. Sea-level fall from the mid-Holocene highstand drove extensive coastal deposition, generating >100,000 km2 of lowlands over the past 6,000 years, with progradation rates of 101–102 m/yr. These geologically young landscapes now face rapid, multidirectional change under contemporary forcing. Coastal change in SEA is complex, and rather than uniform erosion and inundation, the region exhibits a mosaic of responses, from stability to rapid progradation and island migration. Contemporary rates of change are comparable to those documented across the Holocene (102 m/yr), but are responding to a broader suite of drivers, including tectonic deformation, variable RSLR, extreme events and intense human activity. Attribution remains elusive, constrained by sparse spatial coverage, uneven representation of landform types and limited temporal resolution of data. Addressing these gaps requires comprehensive, site-specific studies of both geological and contemporary dynamics across all coastal typologies, supported by high-resolution monitoring and integrated modelling. Such efforts will provide the empirical foundation needed for informed coastal management and adaptation strategies in one of the world’s most vulnerable regions.

This study examined the within- and between-day reliability of commonly employed laboratory-based body composition assessment methods. Eighteen healthy adults reported to the laboratory on two occasions, separated by 1–2 d, and were assessed with multiple methods under standardised conditions. These included two dual-energy X-ray absorptiometry (DXA) scanners with manual or automated regions of interest, air displacement plethysmography (ADP) with measured or estimated thoracic gas volume (TGV), two multi-frequency bioelectrical impedance analysers (MFBIA), single-frequency BIA (SFBIA) and bioimpedance spectroscopy. Within-day reliability was established via immediate test–retest assessments at the first visit (technical error) and between-day reliability by repeating assessments at the second visit (technical plus biological error). Within- and between-day measures were evaluated using technical error of measurement (TEM) and intraclass correlation coefficients (ICC). For body fat percentage, within-day TEM ranged from 0·03 to 0·70 %, with ICC of 0·993–1·000, while between-day ranged from 0·37 to 1·24 %, with ICC of 0·965–0·998. For fat and fat-free mass (FM and FFM), within-day TEM ranged from 0·02 to 0·53 kg, with ICC of 0·998–1·000 for FFM and 0·992–1·000 for FM. Between-day TEM ranged from 0·26 to 0·90 kg for FM and FFM, with ICC of 0·995–0·999 for FFM and 0·955–0·998 for FM. Across metrics, DXA demonstrated the best reliability, followed by one MFBIA and ADP with predicted TGV. Overall, laboratory-based body composition devices provide excellent within- and between-day reliability under standardised conditions, though observed differences in error may influence method selection when tracking small body composition changes.

We study branching Brownian motion with absorption, in which particles undergo Brownian motions and are killed upon hitting the absorption barrier. We prove that the empirical distribution function of the maximum of this process converges almost surely to a randomly shifted Gumbel distribution.

In his article “Paul Samuelson’s Ways to Macroeconomic Dynamics” Mauro Boianovsky has provided an account of the evolution of Samuelson’s attempts to construct a dynamic theory that, because of Samuelson’s centrality to modern economics, verges on being an account of the history of recent thought on the subject. This paper argues that Samuelson’s views should be related not only to the formal dynamic modeling of Ragnar Frisch and Jan Tinbergen but also to the verbal accounts of dynamics and market processes found in work by Alfred Marshall, John Maurice Clark, Edward Chamberlin, and Joseph Schumpeter that he had studied very carefully. Broadening our perspective in this way helps make sense of some otherwise puzzling features of Samuelson’s economics.

Increased dietary specialization has been considered a significant predictor for risk of extinction within the fossil record. However, these interpretations typically come from species-level morphological assessment of diets aggregated across a broad geographic extent. Using the exceptional fossil record of the John Day Formation, we reconstructed dietary niche breadth for the regional community of canids via morphological tooth traits and dental microwear textures to assess how measures of dietary behavior and plasticity might influence species durations. We found that signals of dietary behavior, as inferred from dietary niche breadth estimated via dental microwear textures, showed a stronger relationship with lineage durations than did morphological tooth traits. Specifically, dietary niche breadth was negatively associated with increased species durations. These results suggest the relationship between overall dental morphology and dietary behaviors is more nuanced than previously expected and that the contribution of dietary flexibility irrespective of tooth morphology to extinction risk deserves further attention.