Tight upper bound on the maximum anti-forcing numbers of graphs

Let $G$ be a simple graph with a perfect matching. Deng and Zhang showed that the maximum anti-forcing number of $G$ is no more than the cyclomatic number. In this paper, we get a novel upper bound on the maximum anti-forcing number of $G$ and investigate the extremal graphs. If $G$ has a perfect matching $M$ whose anti-forcing number attains this upper bound, then we say $G$ is an extremal graph and $M$ is a nice perfect matching. We obtain an equivalent condition for the nice perfect matchings of $G$ and establish a one-to-one correspondence between the nice perfect matchings and the edge-involutions of $G$, which are the automorphisms $\alpha$ of order two such that $v$ and $\alpha(v)$ are adjacent for every vertex $v$. We demonstrate that all extremal graphs can be constructed from $K_2$ by implementing two expansion operations, and $G$ is extremal if and only if one factor in a Cartesian decomposition of $G$ is extremal. As examples, we have that all perfect matchings of the complete graph $K_{2n}$ and the complete bipartite graph $K_{n, n}$ are nice. Also we show that the hypercube $Q_n$, the folded hypercube $FQ_n$ ($n\geq4$) and the enhanced hypercube $Q_{n, k}$ ($0\leq k\leq n-4$) have exactly $n$, $n+1$ and $n+1$ nice perfect matchings respectively.Comment: 15 pages, 7 figure

Solving Gravity Anomaly Matching Problem Under Large Initial Errors in Gravity Aided Navigation by Using an Affine Transformation Based Artificial Bee Colony Algorithm

Gravity aided inertial navigation system (GAINS), which uses earth gravitational anomaly field for navigation, holds strong potential as an underwater navigation system. The gravity matching algorithm is one of the key factors in GAINS. Existing matching algorithms cannot guarantee the matching accuracy in the matching algorithms based gravity aided navigation when the initial errors are large. Evolutionary algorithms, which are mostly have the ability of global optimality and fast convergence, can be used to solve the gravity matching problem under large initial errors. However, simply applying evolutionary algorithms to GAINS may lead to false matching. Therefore, in order to deal with the underwater gravity matching problem, it is necessary to improve the traditional evolutionary algorithms. In this paper, an affine transformation based artificial bee colony (ABC) algorithm, which can greatly improve the positioning precision under large initial errors condition, is developed. The proposed algorithm introduces affine transformation to both initialization process and evolutionary process of ABC algorithm. The single-point matching strategy is replaced by the strategy of matching a sequence of several consecutive position vectors. In addition, several constraints are introduced to the process of evolution by using the output characteristics of the inertial navigation system (INS). Simulations based on the actual gravity anomaly base map have been performed for the validation of the proposed algorithm

An in-depth study on the magnetic resonance imaging characteristics of tendon rupture in sports injuries and its correlation with patients' clinical symptoms

Muscle injuries, such as Achilles and quadriceps tendon ruptures, pose a significant challenge in elite sports, accounting for more than 30% of all sports-related injuries. Our primary goal is to investigate the MR imaging characteristics of tendon rupture in sports injuries and their relationship with patients' clinical symptoms. In our retrospective study at Zhejiang University of Traditional Chinese Medicine's Second Affiliated Hospital (Zhejiang Xinhua Hospital), we compared the clinical presentation and MRI results of 106 patients with isolated AT and QT ruptures. In the AT, the enthesis was identified as a common site of bony avulsions (30.2%). In contrast, insertional ruptures were more common in the gastrocnemius heads (69.8% and 66.0%). The low frequency of mid-substance tears (13.2% to 20.8%) demonstrated the central tendon region's inherent tensile strength. The ruptured musculotendinous junctions affected the soleus (20.8%). In QT, bony avulsions play a minor role (5.1% to 11.3%). The patella was the primary site of tears (42.2% - 45.3%), with the Vastus intermedius favoring proximal tears (58.5%). Our examination of AT and QT ruptures across sub-components sheds light on their distinct patterns and the implications for clinical practice in terms of precise diagnosis, personalized treatment, and, ultimately, better patient outcomes for these debilitating injuries

Tight upper bound on the maximum anti-forcing numbers of graphs

Let $G$ be a simple graph with a perfect matching. Deng and Zhang showed that the maximum anti-forcing number of $G$ is no more than the cyclomatic number. In this paper, we get a novel upper bound on the maximum anti-forcing number of $G$ and investigate the extremal graphs. If $G$ has a perfect matching $M$ whose anti-forcing number attains this upper bound, then we say $G$ is an extremal graph and $M$ is a nice perfect matching. We obtain an equivalent condition for the nice perfect matchings of $G$ and establish a one-to-one correspondence between the nice perfect matchings and the edge-involutions of $G$, which are the automorphisms $\alpha$ of order two such that $v$ and $\alpha(v)$ are adjacent for every vertex $v$. We demonstrate that all extremal graphs can be constructed from $K_2$ by implementing two expansion operations, and $G$ is extremal if and only if one factor in a Cartesian decomposition of $G$ is extremal. As examples, we have that all perfect matchings of the complete graph $K_{2n}$ and the complete bipartite graph $K_{n, n}$ are nice. Also we show that the hypercube $Q_n$, the folded hypercube $FQ_n$ ($n\geq4$) and the enhanced hypercube $Q_{n, k}$ ($0\leq k\leq n-4$) have exactly $n$, $n+1$ and $n+1$ nice perfect matchings respectively

Verification of Key Target Molecules for Intramuscular Fat Deposition and Screening of SNP Sites in Sheep from Small-Tail Han Sheep Breed and Its Cross with Suffolk

Intramuscular fat (IMF) is vital for meat tenderness and juiciness. This study aims to explore the IMF deposition mechanism and the related molecular markers in sheep. Two populations, Small-tail Han Sheep (STH) and STH × Suffolk (SFK) F1 (SFK × STH), were used as the research object. Histological staining techniques compared the differences in the longissimus dorsi muscle among populations. A combination of transcriptome sequencing and biological information analysis screened and identified IMF-related target genes. Further, sequencing technology was employed to detect SNP loci of target genes to evaluate their potential as genetic markers. Histological staining revealed that the muscle fiber gap in the SFK × STH F1 was larger and the IMF content was higher. Transcriptome analysis revealed that PIK3R1 and PPARA were candidate genes. Histological experiments revealed that the expressions of PIK3R1 mRNA and PPARA mRNA were lower in SFK × STH F1 compared with the STH. Meanwhile, PIK3R1 and PPARA proteins were located in intramuscular adipocytes and co-located with the lipid metabolism marker molecule (FASN). SNP locus analysis revealed a mutation site in exon 7 of the PIK3R1 gene, which served as a potential genetic marker for IMF deposition. This study’s findings will provide a new direction for meat quality breeding in sheep

The ankle–brachial index and risk of incident stroke in Chinese hypertensive population without atrial fibrillation: A cross‐sectional study

Abstract We aimed to evaluate the relation of the ankle–brachial index (ABI) with the prevalence of stroke and to examine any possible effect modifiers among hypertensive patients without atrial fibrillation. A total of 10 750 subjects with hypertension aged 27‐96 years were included in the current study. The outcome was a stroke. Odds ratios of stroke concerning ABI were calculated using multivariate logistic regression models. Among 10 750 hypertensive participants, 690 (6.42%) had a stroke. Multivariate logistic analyses showed that ABI was negatively correlated with the prevalence of stroke (per SD increment; adjusted OR, 0.88; 95% CI, 0.82‐0.94). Compared with participants in Q 1, the odds ratios (95% CI) for those in the Q2 (1.05 to 1.10), Q3 (1.10 to 1.15), and Q4 (≥1.15) were 0.71 (0.56, 0.90), 0.87 (0.70, 1.08), and 0.81 (0.65, 1.01), respectively. However, compared with higher ABI value, lower ABI value (<1.05) would significantly increase the odds of stroke (OR: 1.26, 95% CI [1.05‐1.50]), especially in the elderly over 65 years old. A generalized additive model and a smooth curve fitting showed that there existed an L‐shaped association between ABI and the prevalence of stroke. Our results suggest that an L‐shaped association between ABI and the prevalence of stroke was found in general hypertensive patients, with a turning point at about 1.05. Compared with higher ABI value, lower ABI value (<1.05) would significantly increase the prevalence of stroke (OR: 1.26, 95% CI [1.05‐1.50]), especially in the elderly over 65 years old