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.

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 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.

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.

Criticism on Wilkie Collins’s Poor Miss Finch (1872) has noted the strong contrasts Collins sets up between binaries such as sight and touch and able-bodiedness and disability. This article proposes that these structuring binaries cohere around three interdependent “problems of knowing”: the near-incommunicability of subjective, embodied experience; the ways in which sensory hierarchies transform normative forms of knowledge into totalizing forms of knowing; and, lastly, the problems of knowing inherent in narrative depictions of lived experience. While sensation fiction has been increasingly reexamined and revalued, much of the radical potential of its embodied reading techniques remains to be explored. This article argues that Poor Miss Finch seeks to bridge the gap created by the three problems of knowing, drawing on sensation fiction’s formal features of melodrama and sudden disruptions of domesticity to create moments of sensory disorientation and heightened affect, enabling imaginative immersion in nonnormative embodied and perceptual experiences.

We study intersecting families of words from the Erdős–Ko–Rado perspective. When the alphabet size is $2$, a maximum intersecting family is not necessarily a star. However, we prove that every maximum $3$-wise intersecting family is a star. We also present a new proof of the known result for alphabets of size at least $3$: maximum intersecting families of words are exactly the stars.

The excavations at Liberty Southwark (LDM21) carried out by Museum of London Archaeology (MOLA) have yielded one of the largest assemblages of Roman wall-painted plaster in London. In the assessment and reassembling of the plasters, the building material specialist discovered two inscriptions unique to Roman Britain and likely to the study of Roman wall paintings in general. Pit (423) yielded what looks to be a signature by the painter while (135) produced a near-complete Greek alphabet scored into the plaster. Both inscriptions were analysed in the greater context of the Roman world in which comparisons of similar inscriptions were made.

This study considers Glomalveolina subtilis Hottinger, 1960, to be a distinct species within the genus Glomalveolina, previously grouped with G. lepidula (Schwager, 1883). This species is distinguished by unique morphological and biometrical features, setting it apart from closely related species and establishing it as a significant biostratigraphic marker for the early Ypresian (SBZ6-7) in the central Neo-Tethys. Although first reported from the Iranian platform, it expands the paleobiogeographic distribution of G. subtilis, with earlier records from the western Neo-Tethys (Mediterranean and North African basins) during the early Ilerdian (SBZ5–SBZ6) and from the eastern Neo-Tethys (China) in the middle Ilerdian (SBZ7–SBZ8). The Alveolina biostratigraphy is correlated with the calcareous nannofossil biostratigraphy, placing it in the middle part of the NP10 Zone. This discovery highlights the broader distribution of G. subtilis and its significance in refining biostratigraphic correlations and understanding foraminiferal evolution during the Paleocene–Eocene transition.

We cannot justifably believe that any currently available actions will have a non-negligible positive influence a billion or more years in the future. I offer three arguments for this thesis. According to the Infinite Washout Argument, given the non-zero chance that your actions will produce infinitely many effects, any finite effects will wash out in expectation. According to the Cluelessness Argument, we cannot justifiably guess what actions are likely to have positive effects in a billion-plus years. We cannot be justified, for example, in thinking that nuclear war or human extinction would be more likely to have bad than good consequences that far into the future. According to the Negligibility Argument, even if we could justifiably guess that some particular action is likelier to have good than bad consequences that far in the future, the odds of good consequences would be negligible due to the compounding of probabilities over time.