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

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

Image_1_Triglyceride–glucose index change and chronic kidney disease progression in a Chinese hypertensive population.pdf

BackgroundThe impact of triglyceride–glucose (TyG) index variations on chronic kidney disease (CKD) progression remains unexplored. To investigate the effects of the TyG index and its dynamic changes on CKD progression.MethodThis prospective cohort study included data from 8,418 hypertensive participants. The exposure variable in this study was defined as the difference between the TyG index at the last visit from that at baseline. The study’s outcome variable was the progression of CKD, defined as follows: for subjects with an estimated glomerular filtration rate (eGFR) ≥60 mL/min, a ≥30% decrease in eGFR with a final follow-up value ResultsDuring a median follow-up period of 48 months, 1077 patients were diagnosed with CKD progression. In the fully adjusted Model 3, patients with a change in the TyG index ConclusionsOur findings suggest that TyG variability may serve as a useful tool for identifying individuals at risk of CKD progression, particularly hypertensive patients with normal DBP levels.</p

Novel 1‑Phenyl-3-hydroxy-4-pyridinone Derivatives as Multifunctional Agents for the Therapy of Alzheimer’s Disease

A series of novel 1-phenyl-3-hydroxy-4-pyridinone derivatives were designed and synthesized as multifunctional agents for Alzheimer’s disease (AD) therapy through incorporation of 3-hydroxy-4-pyridinone moiety from deferiprone into the scaffold of H₃ receptor antagonists. Most of these new compounds displayed designed quadruple functions, H₃ receptor antagonism, Aβ aggregation inhibition, metal ion chelation, and radical scavenging. Especially, the most promising compound <b>5c</b> displayed nanomolar IC₅₀ values in H₃ receptor antagonism with high selectivity, efficient capability to interrupt the formation of Aβ_1–42 fibrils, good copper and iron chelating properties, and more potent 2,2′-azino-bis­(3-ethyl-benzothiazoline-6-sulfonic acid) radical cation (ABTS^•+) scavenging activity than Trolox. Further biological evaluation revealed that it did not show obvious cytotoxicity and hERG potassium channel inhibition at micromolar concentration. In addition, compound <b>5c</b> demonstrated suitable pharmacokinetic properties and acceptable blood–brain barrier (BBB) permeability <i>in vivo</i>. All these results indicate that compound <b>5c</b> is a potential multifunctional candidate for AD therapy