We provide a second-order energy expansion for a gas of N bosonic particles with three-body interactions in the Gross-Pitaevskii regime. We especially confirm a conjecture by Nam, Ricaud, and Triay in [25], where they predict the subleading term in the asymptotic expansion of the ground state energy to be of the order $\sqrt {N}$. In addition, we show that low-energy states satisfy Bose-Einstein condensation with a rate of the order $N^{-\frac {3}{4}}$.

Despite its rich biodiversity, India faces severe environmental challenges due to human activities prioritising immediate gratification over long-term sustainability. Recognising the power of education to address environmental crises, Environmental Education (EE) emerged as a field of study to foster environmental consciousness. Hence, equipping teachers with the knowledge, skills and attitudes to effectively integrate environmental education into their pedagogy is crucial for cultivating sustainable behaviour in students. However, research indicated a significant gap in teacher preparedness to effectively address environmental issues, leaving them ill-equipped to implement related activities and tasks in their classrooms. Using qualitative content analysis, the EE-related courses were analysed to study their status, orientation and responsiveness within three pre-service teacher education programmes. The results of the study showed that most environment-related courses are not compulsory and largely have an anthropocentric orientation with a limited socio-scientific approach. The courses are required to be made responsive toward the contemporary issues and concerns related to Education for Sustainable Development.

With the eastward expansion of the Western Zhou c. 1050 BC, the Jiaodong Peninsula on the north-east coast of modern-day China became part of a large polity. Excavations at Qianzhongzitou, located on this peninsula, are revealing how political control over local populations took place. Here, the authors focus on a sequence of Zhou-period, non-residential platforms, the construction of which signifies new forms of ritual spaces. These types of spaces, also found elsewhere in the region, arguably aided in the state assimilation of local deities, illustrating the critical role that ritual played in political unification of early Chinese states and dynasties.

We prove large and moderate deviations for the output of Gaussian fully connected neural networks. The main achievements concern deep neural networks (i.e. when the model has more than one hidden layer) and hold for bounded and continuous pre-activation functions. However, for deep neural networks fed by a single input, we have results even if the pre-activation is ReLU. When the network is shallow (i.e. there is exactly one hidden layer), the large and moderate principles hold for quite general pre-activation functions.

Phonotactic patterns are commonly constrained by morphology. In English, for example, non-homorganic nasal–stop sequences are disallowed within morphemes but may occur across morpheme boundaries. This article demonstrates that similar effects of morphology on phonotactics can be found with non-concatenative morphology, even though they involve morphological domains that are more difficult to identify on the surface. Specifically, vowel alternation in a class of Egyptian Arabic verbs is affected by gradient phonotactic restrictions on consonant–vowel co-occurrence. However, such restrictions are only active in the imperfective form (e.g., [-rgaʕ] ‘return.ipfv’), not the perfective (e.g., [rigiʕ] ‘return.pfv’). Using a lexicon study and a wug test, I show that this pattern is in fact bounded by morphological domains and is reliably generalised by speakers when deriving novel forms. I compare accounts of this effect that differ on whether they require abstract morphosyntactic representations and non-concatenative morphemes and discuss their implications.

Schubert Vanishing is a problem of deciding whether Schubert coefficients are zero. Until this work it was open whether this problem is in the polynomial hierarchy ${{\mathsf {PH}}}$. We prove this problem is in ${{\mathsf {AM}}} \cap {{\mathsf {coAM}}}$ assuming the Generalized Riemann Hypothesis ($\mathrm{GRH}$), that is, relatively low in ${{\mathsf {PH}}}$. Our approach uses Purbhoo’s criterion [57] to construct explicit polynomial systems for the problem. The result follows from a reduction to Parametric Hilbert’s Nullstellensatz, recently analyzed in [2]. We extend our results to all classical types.

Comparativists (about mass) eliminate absolute masses from the fundamental ontological picture by virtue of a principle of economy, the “Comparative Razor”, which requires that only mass-relations, that are invariant under (metrical) symmetries be considered fundamental. I show how this weapon backfires. If mass-relations are endowed with a standard (multiplicative) concatenation structure, power-transformations become (metrical) symmetries, leaving comparativists prima facie unable to distinguish a possible world and its duplicate where mass-relations are uniformly squared. Then, I considered possible exit strategies, which unfortunately either rely on hidden absolutist assumptions, or leave comparativists and absolutists on equal footing.

San Sebastián del Monte Mixtec (henceforth SSM), also known as Tò’on Ndà’vi, is a language of the Mixtecan family, Otomanguean stock. SSM has lexical tones that are orthogonal to rearticulation on vowels. The aim of this production study is to examine both long modal and rearticulated vowels to gain insight into the SSM tonal system, contrastive voice quality, and any potential interactions between voice quality and f0. Rearticulated vowels are described as having a glottal gesture between two vowels of the same quality (V͡ˀV), while modal vowels have no such gesture (VV). To this end, we examined the phonetic realization of the lexical tones in long modal vowels in terms of f0. All tones are distinguished by f0; f0 patterns largely as expected given previously ascribed labels, with minor deviations. Secondly, the phasing and degree of glottalization in rearticulated vowels was measured using ‘strength of excitation’ (SoE); generally the glottal gesture was vowel medial with a dip in SoE at the beginning of the glottal gesture and a rise in SoE following the glottal gesture. However, there was a large degree of interspeaker variation in the production of rearticulated vowels. Additionally, lexical tone category was found to have an impact on the phasing and degree of glottal gesture in rearticulated vowels, and on voice quality in long modal vowels. This supports the idea that voice quality is an additional correlate of lexical tone in SSM.

We investigate the shape of a tin sheet formed from a droplet struck by a nanosecond laser pulse. Specifically, we examine the dynamics of the process as a function of laser beam properties, focusing on the outstanding puzzle of curvature inversion: tin sheets produced in experiments and state-of-the-art extreme ultraviolet (EUV) nanolithography light sources curve in a direction opposite to previous theoretical predictions. We resolve this discrepancy by combining direct numerical simulations with experimental data, demonstrating that curvature inversion can be explained by an instantaneous pressure impulse with low kurtosis. Specifically, we parametrise a dimensionless pressure width, $ W$, using a raised cosine function and successfully reproduce the experimentally observed curvature over a wide range of laser-to-droplet diameter ratios, $ 0.3 \lt d/D_0 \lt 0.8$. The simulation process described in this work has applications in the EUV nanolithography industry, where a laser pulse deforms a droplet into a sheet, which is subsequently ionised by a second pulse to produce EUV-emitting plasma.

The reuse of information derived from past archaeological investigations is integral to contemporary research practices. Yet, archiving practices of many (but not all) scholars, cultural resource managers, and public agencies often fall short of meeting standard best practices. This limitation impedes efficient and meaningful reuse of information in future research and management endeavors. To alleviate archival and reuse concerns, the development of publicly available, secure, online archives is crucial to improving scholarly research, assisting in land-planning activities and enhancing access to cultural heritage documents for Indigenous communities. In response to these challenges and in collaboration with state, federal, and tribal partners, the Center for Digital Antiquity established the Digital Archive of Huhugam Archaeology. This archive, preserved in the Digital Archaeological Record (tDAR), consolidates information from more than 90 years of archaeological investigations in central and southern Arizona. We outline the process of constructing the archive and describe the current methods for assessing reuse (distinguishing between quantity and quality) and the value of reuse. Even though metrics such as page views and downloads are used often, we believe that when used on their own they fail to adequately capture the true value of reused data for academics, cultural resource managers, Indigenous communities, and the public.