In this paper, we study the existence of solutions to the following Hartree equation

\begin{align*}\begin{cases}-\Delta u+\lambda V(x) u+\mu u=\left(\int_{\mathbb{R}^N}\frac{|u|^p}{|x-y|^{N-\alpha}}\right)|u|^{p-2}u,\ \text{in}\ \mathbb{R}^N,\\\int_{\mathbb{R}^N}|u|^2=\omega,\end{cases}\end{align*}

Where $N\geq 3$, $\omega,\lambda \gt 0$, $p\in \left(\frac{N+\alpha}{N}, \frac{N+\alpha}{N-2}\right)\setminus\left\{\frac{N+\alpha+2}{N}\right\}$ and µ will appear as a Lagrange multiplier. We assume that $0\leq V\in L^{\infty}_{loc}(\mathbb{R}^N)$ has a bottom $int V^{-1}(0)$ composed of $\ell_0$ $(\ell_{0}\geq1)$ connected components $\{\Omega_i\}_{i=1}^{\ell_0}$, where $int V^{-1}(0)$ is the interior of the zero set $V^{-1}(0)=\{x\in\mathbb{R}^N| V(x)=0\}$ of V. It is worth pointing out that the penalization technique is no longer applicable to the local sublinear case $p\in \left(\frac{N+\alpha}{N},2\right)$. Therefore, we develop a new variational method in which the two deformation flows are established that reflect the properties of the potential. Moreover, we find a critical point without introducing a penalization term and give the existence result for $p\in \left(\frac{N+\alpha}{N}, \frac{N+\alpha}{N-2}\right)\setminus\left\{\frac{N+\alpha+2}{N}\right\}$. When ω is fixed and satisfies $\omega^{\frac{-(p-1)}{-Np+N+\alpha+2}}$ sufficiently small, we construct a $\ell$-bump $(1\leq\ell\leq \ell_{0})$ positive normalization solution, which concentrates at $\ell$ prescribed components $\{\Omega_i\}^{\ell}_{i=1}$ for large λ. We also consider the asymptotic profile of the solutions as $\lambda\rightarrow\infty$ and $\omega^{\frac{-(p-1)}{-Np+N+\alpha+2}}\rightarrow 0$.

Due to the lack of explicit word boundary markers, L2-Chinese learners have shown some difficulties in Chinese word segmentation. This study aimed to tackle the possible reasons of L2-Chinese learners’ difficulties in word segmentation: L1-biased processing strategy or developing mental representations of Chinese compound words, or both. In an eye-tracking experiment, high-frequency two-character Chinese compound words were used as targets. These compound words were embedded in sentences where their first component characters with prior verbs were manipulated to be either plausible or implausible, while the whole compound words were always plausible. Sentences were presented in character-spaced or word-spaced style. High-proficiency L2-Chinese learners and native Chinese speakers participated. Results revealed non-native-like patterns of L2-Chinese learners: they holistically processed compound words only in the word-spaced condition, while native speakers did so regardless how sentences were presented. The findings indicated that high-proficiency L2-Chinese learners’ difficulty in word segmentation is predominantly caused by their L1-biased processing strategy.

In this paper, we first describe the cohomology theory of Lie supertriple systems by using the cohomology theory of the associated Leibniz superalgebras. Then we focus on Lie supertriple systems with superderivations, called LSTSDer pairs. We introduce the notion of representations of LSTSDer pairs and investigate their corresponding cohomology theory. We also construct a differential graded Lie algebra whose Maurer–Cartan elements are LSTSDer pairs. Moreover, we consider the relationship between a LSTSDer pair and the associated LeibSDer pair. Furthermore, we develop the 1-parameter formal deformation theory of LSTSDer pairs and prove that it is governed by the cohomology groups. At last, we study abelian extensions of LSTSDer pairs and show that equivalent abelian extensions of LSTSDer pairs are classified by the third cohomology groups.

Weeds significantly reduce sugarcane (Saccharum officinarum L.) production by 30% to 50% and cause complete crop loss in severe cases. Guangxi, a central sugarcane-growing region in southern China, faces significant challenges due to the proliferation of weeds severely impacting crop tillering, yield, and quality. In this study, we surveyed and identified 35 weed species belonging to 16 families in Longzhou, Nongqin, and Qufeng, with significant threats posed by purple nutsedge (Cyperus rotundus L.), bermudagrass [Cynodon dactylon (L.) Pers.], hairy crabgrass [Digitaria sanguinalis (L.) Scop.], black nightshade (Solanum nigrum L.), white-edge morningglory [Ipomoea nil (L.) Roth], and ivy woodrose [Merremia hederacea (Burm. f.) Hallier f.]. The application of 81% MCPA-ametryn-diuron achieved greater than 90% control within 15 d. Although herbicides are effective, they can unintentionally harm sugarcane, indicating a need for tolerant genotypes. Therefore, we comprehensively evaluated herbicide-induced phytotoxic responses and identified tolerant sugarcane genotypes over 3 yr of trials conducted on 222 genotypes across Guangxi. We quantified phytotoxicity by counting the number and severity of affected leaves. The ANOVA revealed statistically significant main and interaction effects among genotype, crop cycle, and location. Cluster and discriminant analyses classified the genotypes into five groups: 21 highly tolerant (HT), 68 tolerant, 75 moderately tolerant, 18 susceptible, and 40 highly susceptible. The 21 HT genotypes demonstrated strong potential to be used as parental lines for breeding herbicide-tolerant varieties, to inform precision breeding strategies, and to increase tolerance to herbicide stress in sugarcane.

Persistent malnutrition is associated with poor clinical outcomes in cancer. However, assessing its reversibility can be challenging. The present study aimed to utilise machine learning (ML) to predict reversible malnutrition (RM) in patients with cancer. A multicentre cohort study including hospitalised oncology patients. Malnutrition was diagnosed using an international consensus. RM was defined as a positive diagnosis of malnutrition upon patient admission which turned negative one month later. Time-series data on body weight and skeletal muscle were modelled using a long short-term memory architecture to predict RM. The model was named as WAL-net, and its performance, explainability, clinical relevance and generalisability were evaluated. We investigated 4254 patients with cancer-associated malnutrition (discovery set = 2977, test set = 1277). There were 2783 men and 1471 women (median age = 61 years). RM was identified in 754 (17·7 %) patients. RM/non-RM groups showed distinct patterns of weight and muscle dynamics, and RM was negatively correlated to the progressive stages of cancer cachexia (r = –0·340, P < 0·001). WAL-net was the state-of-the-art model among all ML algorithms evaluated, demonstrating favourable performance to predict RM in the test set (AUC = 0·924, 95 % CI = 0·904, 0·944) and an external validation set (n 798, AUC = 0·909, 95 % CI = 0·876, 0·943). Model-predicted RM using baseline information was associated with lower future risks of underweight, sarcopenia, performance status decline and progression of malnutrition (all P < 0·05). This study presents an explainable deep learning model, the WAL-net, for early identification of RM in patients with cancer. These findings might help the management of cancer-associated malnutrition to optimise patient outcomes in multidisciplinary cancer care.

The World Cancer Research Fund and the American Institute for Cancer Research recommend a plant-based diet to cancer survivors, which may reduce chronic inflammation and excess adiposity associated with worse survival. We investigated associations of plant-based dietary patterns with inflammation biomarkers and body composition in the Pathways Study, in which 3659 women with breast cancer provided validated food frequency questionnaires approximately 2 months after diagnosis. We derived three plant-based diet indices: overall plant-based diet index (PDI), healthful plant-based diet index (hPDI) and unhealthful plant-based diet index (uPDI). We assayed circulating inflammation biomarkers related to systemic inflammation (high-sensitivity C-reactive protein [hsCRP]), pro-inflammatory cytokines (IL-1β, IL-6, IL-8, TNF-α) and anti-inflammatory cytokines (IL-4, IL-10, IL-13). We estimated areas (cm2) of muscle and visceral and subcutaneous adipose tissue (VAT and SAT) from computed tomography scans. Using multivariable linear regression, we calculated the differences in inflammation biomarkers and body composition for each index. Per 10-point increase for each index: hsCRP was significantly lower by 6·9 % (95 % CI 1·6%, 11·8%) for PDI and 9·0 % (95 % CI 4·9%, 12·8%) for hPDI but significantly higher by 5·4 % (95 % CI 0·5%, 10·5%) for uPDI, and VAT was significantly lower by 7·8 cm2 (95 % CI 2·0 cm2, 13·6 cm2) for PDI and 8·6 cm2 (95 % CI 4·1 cm2, 13·2 cm2) for hPDI but significantly higher by 6·2 cm2 (95 % CI 1·3 cm2, 11·1 cm2) for uPDI. No significant associations were observed for other inflammation biomarkers, muscle, or SAT. A plant-based diet, especially a healthful plant-based diet, may be associated with reduced inflammation and visceral adiposity among breast cancer survivors.

Little is known about the association between iodine nutrition status and bone health. The present study aimed to explore the connection between iodine nutrition status, bone metabolism parameters, and bone disease (osteopenia and osteoporosis). A cross-sectional survey was conducted involving 391, 395, and 421 adults from iodine fortification areas (IFA), iodine adequate areas (IAA), and iodine excess areas (IEA) of China. Iodine nutrition status, bone metabolism parameters and BMD were measured. Our results showed that, in IEA, the urine iodine concentrations (UIC) and serum iodine concentrations (SIC) were significantly higher than in IAA. BMD and Ca2+ levels were significantly different under different iodine nutrition levels and the BMD were negatively correlated with UIC and SIC. Univariate linear regression showed that gender, age, BMI, menopausal status, smoking status, alcohol consumption, UIC, SIC, free thyroxine, TSH, and alkaline phosphatase were associated with BMD. The prevalence of osteopenia was significantly increased in IEA, UIC ≥ 300 µg/l and SIC > 90 µg/l groups. UIC ≥ 300 µg/l and SIC > 90 µg/l were risk factors for BMD T value < –1·0 sd. In conclusion, excess iodine can not only lead to changes in bone metabolism parameters and BMD, but is also a risk factor for osteopenia and osteoporosis.

Although it is well established that gestational diabetes mellitus (GDM) is associated with fetal overgrowth in singleton pregnancies, little is known about its role in twins. We aimed to explore the relationship between GDM and the longitudinal fetal growth in twin pregnancies. This was a retrospective matched cohort study of GDM and non-GDM twin pregnancies delivered ≥36 weeks without other complications. All the women performed ≥3 ultrasounds after 22 weeks. Linear mixed models (LMMs) were used to explore the relationships between longitudinal fetal growth trajectories and GDM. Group-based trajectory modeling (GBTM) and generalized estimating equation (GEE) were applied to identify the latent growth patterns and investigate their relationships with GDM. In total, 215 GDM and 645 non-GDM twins were included, the majority of the patients did not require medication therapy (n = 202, GDMA1). LMM revealed that, compared with non-GDM, GDM was associated with an average increase in fetal weight of 4.36 g (95% CI [1.25, 7.48]) per week. GBTM and GEE further revealed that GDM increased the odds of fetal weight trajectory to nearly 40% of the total fetal weight trajectory, classified into the high-speed group (aOR = 1.39, 95% CI [1.03, 1.88]), associating with a 49.44 g (95% CI [11.41, 87.48]) increase in birth weight. Subgroup analysis revealed that all these differences were only significant among the GDMA1 pregnancies (p < .05). GDM (GDMA1) is significantly associated with an increase in fetal weight during gestation in twin pregnancies. However, this acceleration is mild, and its significance requires further exploration.

The Hele-Shaw–Cahn–Hilliard model, coupled with phase separation, is numerically simulated to demonstrate the formation of anomalous fingering patterns in a radial displacement of a partially miscible binary-fluid system. The composition of injected fluid is set to be less viscous than the displaced fluid and within the spinodal or metastable phase-separated region, in which the second derivative of the free energy is negative or positive, respectively. Because of phase separation, concentration evolves non-monotonically between the injected and displaced fluids. The simulations reveal four areas of the concentration distribution between the fluids: the inner core; the low-concentration grooves/high-concentration ridges; the isolated fluid fragments or droplets; the mixing zone. The grooves/ridges and the fragments/droplets, which are the unique features of phase separation, form in the spinodal and metastable regions. Four typical types of patterns are categorized: core separation (CS); fingering separation (FS); separation fingering (SF); lollipop fingering, in the order of the dominance of phase separation, respectively. For the patterns of CS and FS, isolated fluid fragments or droplets around the inner core are the main features. Fingering formation is better maintained with droplets in the SF pattern if the phase separation is relatively weaker than viscous fingering (VF). Even continuous fingers are well preserved in the case of dominant VF; phase separation results in lollipop-shaped fingers. The evolving trend of the patterns is in line with the experiments. These patterns are summarized in a pattern diagram, mainly by the magnitude of the second derivative of the free energy profile.

In this paper, we first introduce the concept of symmetric biderivation radicals and characteristic subalgebras of Lie algebras and study their properties. Based on these results, we precisely determine biderivations of some Lie algebras including finite-dimensional simple Lie algebras over arbitrary fields of characteristic not $2$ or $3$, and the Witt algebras $\mathcal {W}^+_n$ over fields of characteristic $0$. As an application, commutative post-Lie algebra structure on the aforementioned Lie algebras is shown to be trivial.

Fiber Bragg grating-based Raman oscillators are capable of achieving targeted frequency conversion and brightness enhancement through the provision of gain via stimulated Raman scattering across a broad gain spectrum. This capability renders them an exemplary solution for the acquisition of high-brightness, specialized-wavelength lasers. Nonetheless, the output power of all-fiber Raman oscillators is typically limited to several hundred watts, primarily due to limitations in injectable pump power and the influence of higher-order Raman effects, which is inadequate for certain application demands. In this study, we introduce an innovative approach by employing a graded-index fiber with a core diameter of up to 150 μm as the Raman gain medium. This strategy not only enhances the injectable pump power but also mitigates higher-order Raman effects. Consequently, we have successfully attained an output power of 1780 W for the all-fiber Raman laser at 1130 nm, representing the highest output power in Raman fiber oscillators with any configuration reported to date.

Tryptophan (Trp) is an essential amino acid acting as a key nutrition factor regulating animal growth and development. But how Trp modulates food intake in pigs is still not well known. Here, we investigated the effect of dietary supplementation of Trp with different levels on food intake of growing pigs. The data showed that dietary Trp supplementation with the standardised ileal digestibility (SID) Trp to lysine (Lys) ratio at both 0·18 and 0·20 significantly increased the food intake by activating the expression of orexigenic gene agouti-related peptide (AgRP) and inhibiting the expression of anorexigenic gene pro-opiomelanocortin (POMC), cocaine- and amphetamine-regulated transcript (CART) and melanocortin receptor 4 (MC4R) in the hypothalamus. Meanwhile, the level of anorexigenic hormones appetite-regulating peptide YY (PYY) in the duodenum and serum and leptin receptor in the duodenum were also significantly decreased. Importantly, both the kynurenine and serotonin metabolic pathways were activated upon dietary Trp supplementation to downregulate MC4R expression in the hypothalamus. Further mechanistic studies revealed that the reduced MC4R expression activated the hypothalamic AMP-activated protein kinase (AMPK) pathway, which in turn inhibited the mammalian target of rapamycin (mTOR)/S6 kinase 1 (S6K1) activity to stimulate food intake. Together, our study unravels the orexigenic effect of dietary Trp supplementation in pigs and expands its potential application in developing nutrition intervention strategy in pig production.

The impact of a chemical reaction, $A+B \rightarrow C$, on the stability of a miscible radial displacement in a porous medium is established. Our study involves a comprehensive analysis employing both linear stability analysis and nonlinear simulations. Through linear stability analysis, the onset of instability for monotonic as well as non-monotonic viscosity profiles corresponding to the same end-point viscosity are discussed and compared. We establish a $(R_b,R_c)$ phase plane for a wide range of Damköhler number ($Da$) and Péclet number ($Pe$) into stable and unstable regions. Here, $R_b=\ln (\mu _B/ \mu _A)$ and $R_c=\ln (\mu _C/ \mu _A)$ and $\mu _{i}$ is the viscosity of fluid $i$ $\in \{A$, $B$, $C$}. The stable zone in the $(R_b, R_c)$ phase plane contracts with increased $Da$ and $Pe$ but never vanishes. It exists even for $Da \rightarrow \infty$. Interestingly, we obtain a $Da$ independent stable region in the neighbourhood of $R_c=R_b$ where no transition occurs in stability despite changes in reaction rate. The study allows us to acquire knowledge about the transition of the stability for varying $Da, Pe$ and different reactions classified using $R_b, R_c$.

Introduction: Late-life depression (LLD) is associated with cognitive deficit with risk of future dementia. By examining the entropy of the spontaneous brain activity, we aimed to understand the neural mechanism pertaining to cognitive decline in LLD.

Methods: We collected MRI scans in older adults with LLD (n = 32), mild cognitive impairment [MCI (n = 25)] and normal cognitive function [NC, (n = 47)]. Multiscale entropy analysis (MSE) was applied to resting-state fMRI data. Under the scale factor (tau) 1 and 2, reliable separation of fMRI data and noise was achieved. We calculated the brain entropy in 90 brain regions based on automated anatomical atlas (AAL). Due to exploratory nature of this study, we presented data of group-wise comparison in brain entropy between LLD vs. NC, MCI vs. NC, and LLD and MCD with a p-value below 0.001.

Results: The mean Mini-Mental State Examination (MMSE) score of LLD and MCI was 27.9 and 25.6. Under tau 2, we found higher brain entropy of LLD in left globus pallidus than MCI (p = 0.002) and NC (p = 0,009). Higher brain entropy of LLD than NC was also found in left frontal superior gyrus, left middle superior gyrus, left amygdala and left inferior parietal gyrus. The only brain region with higher brain entropy in MCI than control was left posterior cingulum (p-value = 0.015). Under tau 1, higher brain entropy was also found in LLD than in MCI in right orbital part of medial frontal gyrus and left globus pallidus (p-value = 0.007 and 0.005).

Conclusions: Our result is consistent with prior hypothesis where higher brain entropy was found during early aging process as compensation. We found such phenomenon particular in left globus pallidus in LLD, which could be served as a discriminative brain region. Being a key region in reward system, we hypothesis such region may be associated with apathy and with unique pathway of cognitive decline in LLD. We will undertake subsequent analysis longitudinally in this cohort

Key words: resting-state fMRI, Late-life depression, Brain entropy, globus pallidus, cognitive decline