Spectral extremal problem on tt copies of ℓ\ell-cycle

Denote by $tC_\ell$ the disjoint union of $t$ cycles of length $\ell$. Let $ex(n,F)$ and $spex(n,F)$ be the maximum size and spectral radius over all $n$-vertex $F$-free graphs, respectively. In this paper, we shall pay attention to the study of both $ex(n,tC_\ell)$ and $spex(n,tC_\ell)$. On the one hand, we determine $ex(n,tC_{2\ell+1})$ and characterize the extremal graph for any integers $t,\ell$ and $n\ge f(t,\ell)$, where $f(t,\ell)=O(t\ell^2)$. This generalizes the result on $ex(n,tC_3)$ of Erd\H{o}s [Arch. Math. 13 (1962) 222--227] as well as the research on $ex(n,C_{2\ell+1})$ of F\"{u}redi and Gunderson [Combin. Probab. Comput. 24 (2015) 641--645]. On the other hand, we focus on the spectral Tur\'{a}n-type function $spex(n,tC_{\ell})$, and determine the extremal graph for any fixed $t,\ell$ and large enough $n$. Our results not only extend some classic spectral extremal results on triangles, quadrilaterals and general odd cycles due to Nikiforov, but also develop the famous spectral even cycle conjecture proposed by Nikiforov (2010) and confirmed by Cioab\u{a}, Desai and Tait (2022).Comment: 25 pages, one figur

Research progress of quercetin in cardiovascular disease

Quercetin is one of the most common flavonoids. More and more studies have found that quercetin has great potential utilization value in cardiovascular diseases (CVD), such as antioxidant, antiplatelet aggregation, antibacterial, cholesterol lowering, endothelial cell protection, etc. However, the medicinal value of quercetin is mostly limited to animal models and preclinical studies. Due to the complexity of the human body and functional structure compared to animals, more research is needed to explore whether quercetin has the same mechanism of action and pharmacological value as animal experiments. In order to systematically understand the clinical application value of quercetin, this article reviews the research progress of quercetin in CVD, including preclinical and clinical studies. We will focus on the relationship between quercetin and common CVD, such as atherosclerosis, myocardial infarction, ischemia reperfusion injury, heart failure, hypertension and arrhythmia, etc. By elaborating on the pathophysiological mechanism and clinical application research progress of quercetin's protective effect on CVD, data support is provided for the transformation of quercetin from laboratory to clinical application

Surgical treatment of patellar dislocation: A network meta-analysis of randomized control trials and cohort studies

BackgroundCurrently, there are many surgical options for patellar dislocation. The purpose of this study is to perform a network meta-analysis of the randomized controlled trials (RCTs) and cohort studies to determine the better treatment.MethodWe searched the Pubmed, Embase, Cochrane Central Register of Controlled Trials, Web of Science, clinicaltrials.gov and who.int/trialsearch. Clinical outcomes included Kujala score, Lysholm score, International Knee Documentation Committee (IKDC) score, redislocation or recurrent instability. We conducted pairwise meta-analysis and network meta-analysis respectively using the frequentist model to compare the clinical outcomes.ResultsThere were 10 RCTs and 2 cohort studies with a total of 774 patients included in our study. In network meta-analysis, double-bundle medial patellofemoral ligament reconstruction (DB-MPFLR) achieved good results on functional scores. According to the surface under the cumulative ranking (SUCRA), DB-MPFLR had the highest probabilities of their protective effects on outcomes of Kujala score (SUCRA 96.5 %), IKDC score (SUCRA 100.0%) and redislocation (SUCRA 67.8%). However, DB-MPFLR (SUCRA 84.6%) comes second to SB-MPFLR (SUCRA 90.4%) in Lyshlom score. It is (SUCRA 70%) also inferior to vastus medialis plasty (VM-plasty) (SUCRA 81.9%) in preventing Recurrent instability. The results of subgroup analysis were similar.ConclusionOur study demonstrated that MPFLR showed better functional scores than other surgical options

Unary Non-Structural Fertilizer Response Model for Rice Crops and Its Field Experimental Verification

The quadratic polynomial fertilizer response model (QPFM) is the primary method for implementing quantitative fertilization in crop production, but the success rate of this model's recommended fertilization rates in China is low because the model contains a high setting bias. This paper discusses a new modelling method for expanding the applicability of QPFM. The results of field experiments with 8 levels of N, P, or K fertilization showed that the dynamic trend between rice yield increases and fertilizer application rate exhibited a typical exponential relationship. Therefore, we propose a unary non-structural fertilizer response model (NSFM). The responses of 18 rice field experiments to N, P, or K fertilization indicated that the new models could significantly predict rice yields, while two experimental fitting results using the unary QPFM did not pass statistical significance tests. The residual standard deviations of 13 new models were significantly lower than that of the unary QPFM. The linear correlation coefficient of the recommended application rates between the new model and the unary QPFM reached a significant level. Theoretical analysis showed that the unary QPFM was a simplified version of the new model, and it had a higher fitting precision and better applicability

Improving Rice Modeling Success Rate with Ternary Non-structural Fertilizer Response Model

Fertilizer response modelling is an important technical approach to realize metrological fertilization on rice. With the goal of solving the problems of a low success rate of a ternary quadratic polynomial model (TPFM) and to expand the model's applicability, this paper established a ternary non-structural fertilizer response model (TNFM) based on the experimental results from N, P and K fertilized rice fields. Our research results showed that the TNFM significantly improved the modelling success rate by addressing problems arising from setting the bias and multicollinearity in a TPFM. The results from 88 rice field trials in China indicated that the proportion of typical TNFMs that satisfy the general fertilizer response law of plant nutrition was 40.9%, while the analogous proportion of TPFMs was only 26.1%. The recommended fertilization showed a significant positive linear correlation between the two models, and the parameters N-0, P-0 and K-0 that estimated the value of soil supplying nutrient equivalents can be used as better indicators of yield potential in plots where no N or P or K fertilizer was applied. The theoretical analysis showed that the new model has a higher fitting accuracy and a wider application range

Rehabilitation effect of intelligent rehabilitation training system on hemiplegic limb spasms after stroke

This article aimed to explore the rehabilitation efficacy of intelligent rehabilitation training systems in hemiplegic limb spasms after stroke and provided more theoretical basis for the application of intelligent rehabilitation systems in the rehabilitation of hemiplegic limb spasms after stroke. To explore the rehabilitation efficacy of intelligent rehabilitation training system (RTS for short here) in post-stroke hemiplegic limb spasms, this study selected 99 patients with post-stroke hemiplegic limb spasms admitted to a local tertiary hospital from March 2021 to March 2023 as the research subjects. This article used blind selection to randomly divide them into three groups: control group 1, control group 2, and study group, with 33 patients in each group. Control group 1 used a conventional RTS, group 2 used the brain–computer interface RTS from reference 9, and research group used the intelligent RTS from this article. This article compared the degree of spasticity, balance ability score, motor function score, and daily living activity score of three groups of patients after 10 weeks of treatment. After 10 weeks of treatment, the number of patients in the study group with no spasms at level 0 (24) was significantly higher than the number of patients in group 1 (7) and group 2 (10), with a statistically significant difference (P < 0.05); In the comparison of Barthel index scores, after ten weeks of treatment, the total number of people in the study group with scores starting at 71–80 and 81–100 was 23. The total number of people in the score range of 71–80 and 81–100 in group 1 was 5, while in group 2, the total number of people in this score range was 8. The study group scored considerably higher than the control group and the difference was found to be statistically relevant (P < 0.05). In the Berg balance assessment scale and motor function assessment scale, after 10 weeks of treatment, the scores of the study group patients on both scales were significantly higher than those of group 1 and group 2 (P < 0.05). The intelligent RTS is beneficial for promoting the improvement of spasticity in stroke patients with hemiplegic limb spasms, as well as improving their balance ability, motor ability, and daily life activities. Its rehabilitation effect is good

LPS Pretreatment Attenuates Cerebral Ischaemia/Reperfusion Injury by Inhibiting Inflammation and Apoptosis

Background/Aims: Lipopolysaccharide (LPS) pretreatment has a strong neuroprotective effect on cerebral ischaemia/reperfusion injury (IRI), but the mechanism has not been fully elucidated to date. This study investigated the effect of LPS pretreatment on the pathway mediated by endoplasmic reticulum (ER) stress–CCAAT/enhancer-binding protein- homologous protein (CHOP) and the role of this pathway on cerebral ischaemia/reperfusion (I/R)-induced inflammation and apoptosis. Methods: Healthy male BALB/c mice were randomised into four groups as follows: sham operation group (sham group, n=30); LPS group (BALB/c mice treated with LPS, n=30); ischaemia/reperfusion group (I/R group, n=30) and I/R+LPS group (BALB/c mice treated with LPS before ischaemia, n=30). The mice were pre-treated with LPS (0.2 mg/kg) intra-peritoneally for three days prior to cerebral ischaemia. After 24 hours, the neurological deficit score, TTC staining and TUNEL assay were used to assess the neuroprotective effect of the LPS pretreatment against cerebral IRI. To assess whether the ER stress-CHOP pathway participated in the LPS-pretreatment neuroprotective mechanism, the expression levels of related proteins (GRP78, CHOP, caspase-12 and caspase-3) from the ischaemic cortical penumbra were detected via a western blot analysis. An immunohistochemical study was used to detect the expression and location of CHOP in the cortical penumbra. To further assess the protective effect of the LPS pretreatment, the concentrations of inflammatory factors (TNF-α, IL-6, IL-1β and IL-10) in the cortical penumbra were measured by ELISA, and ER stress-CHOP pathway inflammation-related caspase-11 was analysed through western blot analysis. Results: As demonstrated by the experiments, the pretreatment with LPS significantly reduced the neurological deficit score and the infarct size of cerebral IRI. The expression levels of ER stress-CHOP pathway related proteins (GRP78, CHOP, caspase-12 and caspase-3) from the cortical penumbra were significantly decreased by LPS, as well as the level of apoptosis in the cells in the brain. Immunohistochemistry showed that the expression of CHOP significantly decreased after the LPS pretreatment. Furthermore, the concentrations of inflammatory factors (TNF-α, IL-1β, IL-6) were reduced after the LPS pretreatment, whereas the anti-inflammatory cytokine IL-10 was upregulated. In addition, ER stress-CHOP pathway inflammation-related caspase-11 expression was significantly suppressed after the pretreatment with LPS. Conclusions: LPS pretreatment significantly ameliorates the effects of cerebral IRI by inhibiting inflammation and apoptosis, and the potential mechanism of the neuroprotective effect may be associated with the ER stress-CHOP mediated signalling pathway