The famous Sidorenko’s conjecture asserts that for every bipartite graph $H$, the number of homomorphisms from $H$ to a graph $G$ with given edge density is minimised when $G$ is pseudorandom. We prove that for any graph $H$, a graph obtained from replacing edges of $H$ by generalised theta graphs consisting of even paths satisfies Sidorenko’s conjecture, provided a certain divisibility condition on the number of paths. To achieve this, we prove unconditionally that bipartite graphs obtained from replacing each edge of a complete graph with a generalised theta graph satisfy Sidorenko’s conjecture, which extends a result of Conlon, Kim, Lee and Lee [J. Lond. Math. Soc., 2018].

Sentences written in Chinese are composed of continuous sequences of characters, without spaces or other visual cues to mark word boundaries. While skilled L1 readers can efficiently segment this naturally unspaced text into words, little is known about the word segmentation capabilities of L2 readers, including whether they employ the same strategies to process temporary segmental ambiguities. Accordingly, we report two eye movement experiments that investigated the processing of sentences containing temporarily ambiguous “incremental” three-character words (e.g., “体育馆,” meaning “stadium”) whose first two characters could also form a word (“体育,” meaning “sport”), comparing the performance of 48 skilled L1 Chinese readers and 48 high-proficiency L2 Chinese readers in each experiment. Our findings reveal that both groups can process this ambiguity efficiently, employing similar word segmentations strategies. We discuss our findings in relation to models of eye movement control and word recognition in Chinese reading.

Computer vision-based precision weed control has proven effective in reducing herbicide usage, lowering weed management costs, and enhancing sustainability in modern agriculture. However, developing deep learning models remains challenging due to the effort required for weed dataset annotation and the difficulty of identifying weeds at different stages and densities in complex field conditions. To address these challenges, this study introduces an indirect weed detection method that combines deep learning and image processing techniques. The proposed approach first employs an object detection network to identify and label crops within the images. Subsequently, image processing techniques are applied to segment the remaining green pixels, thereby enabling indirect detection of weeds. Furthermore, a novel detection network–CD-YOLOv10n (You Only Look Once version 10 nano)–was developed based on the YOLOv10 framework to optimize computational efficiency. By redesigning the backbone (C2f-DBB) and integrating an optimized upsampling module (DySample), the network achieved higher detection accuracy while maintaining a lightweight structure. Specifically, the model achieved a mean average precision (mAP50) of 98.1%, which is a 1.4% percentage-point increase compared with the YOLOv10n baseline, a relevant improvement given the already strong baseline performance. At the same time, compared to YOLOv10n, its GFLOPs were reduced by 22.62%, and the number of parameters decreased by 15.87%. These innovations make CD-YOLOv10n highly suitable for deployment on resource-constrained platforms.

Entrepreneurial reentry after business failure is an important area of research in the field of entrepreneurship. However, previous studies have largely overlooked the crucial role of time factors – both objective and subjective – in the context of failure and subsequent entrepreneurial endeavors. This study aims to fill this gap by examining the impact of firm lifespan on entrepreneurial reentry and the moderating effect of entrepreneurs’ temporal focus. Through manual matching across multiple databases, we obtain a sample of 368 entrepreneurs. The results show that a longer firm lifespan negatively influences entrepreneurial reentry and that a past focus further amplifies this negative relationship. This study contributes to research on the determinants of entrepreneurial reentry and provides theoretical insights into the role of time in entrepreneurial reentry.

We examine how ambient temperature $T$ (23–90 $^\circ \mathrm{C}$) alters the dynamics of spark-induced cavitation bubbles across a range of discharge energies. As $T$ rises, the collapse of an isolated spherical bubble weakens monotonically, as quantified by the Rayleigh collapse factor, minimum volume and maximum collapse velocity. When the bubble is generated near a rigid wall, the same thermal attenuation is reflected in reduced jet speed and diminished migration. Most notably, at $T \gtrsim 70\,^\circ \text{C}$, we observe a previously unreported phenomenon: secondary cavitation nuclei appear adjacent to the primary bubble interface where the local pressure falls below the Blake threshold. The pressure reduction is produced by the over-expansion of the primary bubble itself, not by rarefaction waves as suggested in earlier work. Coalescence between these secondary nuclei and the parent bubble seeds pronounced surface wrinkles that intensify Rayleigh–Taylor instability and promote fission, providing an additional route for collapse strength attenuation. These findings clarify the inception mechanism of high-temperature cavitation and offer physical insight into erosion mitigation in heated liquids.

This study evaluated the effect of different medium-chain to long-chain fatty acid (MCFA:LCFA, M:L) ratios on growth performance, intestinal function, antioxidant capacity and gut microbiota in piglets. A total of 250 piglets were randomly assigned to five groups with five replicates, each containing ten pigs. The diets, containing varying amounts of MCFA-rich coconut oil and LCFA-rich soyabean oil, resulted in M:L ratios of 0, 2·1, 4·2, 8·8 and 33·8 %. Results showed that both final body weight and average daily weight gain increased as the M:L ratio increased (P < 0·05), while the 8·8 % M:L ratio diet exhibited the lowest feed:gain ratio (P < 0·05). As the M:L ratio increased, the contents of superoxide dismutase and glutathione peroxidase were increased, and MDA was decreased in serum (P < 0·05). The 8·8 and 33·8 % M:L diets improved ileal and jejunal morphology (P < 0·05), as indicated by greater villus height and villus height:crypt depth ratios. Furthermore, increasing M:L ratios from 0 to 33·8 % increased expression of tight junction proteins occludin and ZO-1 in the jejunum (P < 0·05). The 33·8 % M:L ratio reduced microbial α-diversity (P < 0·05), while 8·8 % M:L diet significantly increased the abundance of beneficial bacteria (e.g. Lactobacilli, Prevotella) and decreased harmful bacteria (e.g. Escherichia-Shigella, Enterococcus) in the cecum (P < 0·05). In summary, our study found that 8·8 % of dietary M:L ratios significantly improved growth performance, likely through modulating intestinal function, antioxidant activity and gut microbial composition.

In the context of an aging population and declining birth rates, the advantages of robotic-assisted training are becoming increasingly prominent. However, improving the adaptability and safety of assistive walking robots remains a critical challenge. Accurately identifying a user’s turning intent is essential for preventing dangerous situations such as falls or slips. As one of the core parameters of lower limb motion, foot rotation angles not only reflect the stability and coordination of gait but are also crucial for accurately predicting walking intentions, such as straight walking and turning. This study proposes a gated recurrent unit-based model for predicting foot rotation angles, driven by 3D visual data. By constructing a lower limb linkage model that includes foot joints and incorporating 3D foot rotation angle features, we develop a real-time algorithm for gait state prediction. This model enables accurate prediction of walking intentions, such as straight walking or turning, during walking and is experimentally validated using a robotic walker. The experimental results demonstrate the effectiveness of the proposed predictive model.

The propagation of detonations in a non-uniform mixture exhibits notable distinctions from that in a uniform mixture. This study first delves into the analytical analysis of the one-dimensional shock transmission problem and the two-dimensional shock propagation in a mixture with temperature non-uniformity. Additionally, the research extends to the numerical simulation of the propagation of shocks and detonations, building upon the insights garnered from the analytical analysis. The numerical results indicate that introducing a temperature interface in a non-uniform gas creates a discrete flow field and wavefront, resulting in oblique shocks that connect hot and cold layers. A competitive mechanism between the transverse waves and non-uniformity is responsible for the detonation propagation. The temperature amplitude tends to inhibit the propagation of transverse waves. In contrast, the wavelengths primarily affect the spacing and strength of these transverse waves, especially during the early stages of propagation. In a Zel’Dovich–von Neumann–Döring detonation, the non-uniformities distort the detonation front, creating transverse wave spacings comparable to the wavelength and reducing the front velocity. However, the detonation can recover its Chapman–Jouguet velocity and approach a steady states as intrinsic instabilities come into play. In the steady state, the cell sizes are found to be determined by the temperature amplitude. When the temperature amplitude is sufficiently high, the detonation cells effectively disappear.

This study reports potassium (K) isotope compositions of diamondiferous kimberlites. Altered kimberlite samples exhibit δ41K values ranging from −1.293 ± 0.052 (2SD) to −0.114 ± 0.029 ‰, showing covariations with chemical indicators of alteration. This is consistent with the geochemical dynamics of K isotopes in hydrothermal fluid-related processes. In contrast, pristine kimberlite samples display restricted K isotope compositions, with δ41K values between −0.494 ± 0.057 and −0.270 ± 0.048 ‰. Notably, the δ41K values of these pristine kimberlite samples correlate well with K2O and Rb contents, suggesting that approximately ∼0.2 ‰ of K isotope fractionation is induced by phlogopite crystallization, as indicated by quantitative modelling. The estimated δ41K values of −0.458 ‰ for the primary kimberlite melt and of −0.414 ‰ for the kimberlite source imply a potential link to the bulk silicate Earth. These new measurements, along with literature data from various rocks, indicate that the K isotope composition in the deep mantle (>150 km) is more homogenous than in shallow regions, likely reflecting the efficiency of convection flow and K behaviour during subduction. In addition, the K isotope data reveal temporal variations in mantle-derived magmas from the Palaeozoic to the Cenozoic, highlighting the geological history and lithospheric destruction of the North China Craton. This study underscores the significance of K isotopes in enhancing our understanding of mantle dynamics, crustal recycling and the geochemical evolution of the Earth’s interior.

In this paper, a highly integrated wideband 3 × 3 Nolen Matrix with inherent filtering characteristics is proposed. It is based on an arbitrary-phase-difference (A-PD) filtering coupler and phase compensation networks. The proposed A-PD filtering coupler, composed of three groups of coupled lines, offers outstanding advantages, including wide bandwidth, flat output distributions, high frequency selectivity, and compact structure. To address the challenges introduced by the series topology of the Nolen matrix, a differential phase shift network and a phase slope adjustment network are incorporated, ensuring a constant phase difference between stages and minimizing in-band phase errors at the output ports. By integrating the A-PD filtering coupler with the phase compensation networks, a compact Nolen matrix centered at 3.5 GHz is realized, occupying only 0.5 λg × 0.5 λg. Measurement results validate its excellent performance, demonstrating an overlapping bandwidth exceeding 50% under the criteria of 10-dB return loss, 3-dB passband, ±1 dB amplitude imbalance, and ±5° phase difference error. Furthermore, the design achieves over 15 dB stopband rejection.

In the realm of data-to-text generation tasks, the use of large language models (LLMs) has become common practice, yielding fluent and coherent outputs. Existing literature highlights that the quality of in-context examples significantly influences the empirical performance of these models, making the efficient selection of high-quality examples crucial. We hypothesize that the quality of these examples is primarily determined by two properties: their similarity to the input data and their diversity from one another. Based on this insight, we introduce a novel approach, Double Clustering-based In-Context Example Selection, specifically designed for data-to-text generation tasks. Our method involves two distinct clustering stages. The first stage aims to maximize the similarity between the in-context examples and the input data. The second stage ensures diversity among the selected in-context examples. Additionally, we have developed a batched generation method to enhance the token usage efficiency of LLMs. Experimental results demonstrate that, compared to traditional methods of selecting in-context learning samples, our approach significantly improves both time efficiency and token utilization while maintaining accuracy.