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The edit distance function of a hereditary property 𝒣 is the asymptotically largest edit distance between a graph of density p ∈ [0, 1] and 𝒣. Denote by Pn and Cn the path graph of order n and the cycle graph of order n, respectively. Let C2n*C_{2n}^* be the cycle graph C2n with a diagonal, and C˜n{\tilde C_n} be the graph with vertex set {v0, v1, . . . , vn−1} and E(C˜n)=E(Cn)∪{v0v2}E\left( {{{\tilde C}_n}} \right) = E\left( {{C_n}} \right) \cup \left\{ {{v_0}{v_2}} \right\}. Marchant and Thomason determined the edit distance function of C6*C_6^*. Peck studied the edit distance function of Cn, while Berikkyzy et al. studied the edit distance of powers of cycles. In this paper, by using the methods of Peck and Martin, we determine the edit distance function of C8*C_8^*, C˜n{\tilde C_n} and Pn, respectively.

Abstract Backgroud This study aimed to explore the clinical value of long - term electroencephalogram (LTM EEG) in seizure-free individuals taking antiepileptic drugs (AEDs) for more than 2 years. We try to look for clinical factors associated with epileptiform activity on LTM EEG in seizure free patients. We hope that the detection of epileptiform activity by the LTM EEG recording can develop the better treatment strategy. Methods The LTM EEG recordings of 770 individuals with a definite diagnosis of epilepsy were assessed. Two hundred sixty-two individuals accorded with the inclusion criteria and exclusion criteria. We collect the demographic and clinical information and LTM EEG data of these 262 individuals. We analysed the data by one-way analysis of variance and Cox proportional hazards models. Results We found that more epileptiform activity were found with LTM EEG recording than regular EEG recording in seizure-free individuals. We found several clinical factors could be associated with epileptiform activity on LTM EEG in seizure free patients by a one-way analysis: symptomatic or cryptogenic epilepsy [hazard ratio (HR) = 2.6], history of cerebral trauma (HR = 7.5), and abnormal imaging findings (HR = 3.1). The following factors suggested a correlation between history of cerebral trauma (HR = 2.4) and history of cerebral surgery (HR = 3.4) with epileptiform activity on LTM EEG presentation by multivariate logistic regression analysis. Conclusions The study indicated a correlation of a number of factors with abnormal LTM EEG presentation: symptomatic or cryptogenic epilepsy, history of cerebral trauma, history of cerebral surgery, and abnormal imaging findings. The LTM EEG recording may help find epileptiform activity in high risk seizure-free individuals. The individuals need be reevaluated the therapeutic strateagies, and increase the hope to reach real seizure-free.

Evidence on the association of 25‐hydroxyvitamin D (25[OH]D) and obesity during the first 5 years of life is limited in China. The objective of this study was to examine the associations between weight, weight for age z score (ZWAZ), weight for length/height z score (ZWHZ), and body mass index for age z score (ZBMI) and 25(OH)D. This was a large population‐based cross‐sectional multicenter study in which the children aged 0–5 years were recruited from 12 children's healthcare centers by a stratified cluster random‐sampling method in 10 cities of the Jiangsu province, China. The 25(OH)D concentration was determined by ELISA. A total of 5289 children were investigated. For 0–71 months children with obesity and nonobesity, the prevalence of vitamin D deficiency was 36.0% and 29.8%, and the 25(OH)D level was 59.8 and 64.0 nmol/L, respectively, and there were all significant difference. Compared with children with nonobesity, children with obesity had higher risk of vitamin D deficiency (OR [95% CI]: 1.33 [1.02, 1.72], p <.05), and had lower 25(OH)D level (β = −3.84, 95% CI = −7.58, −0.09, p <.05). The results for children aged 24–71 months were similar to those for children aged 0–71 months. However, no significant difference was observed in children aged 0–23 months. Vitamin D deficiency was observed in children with greater adiposity during the first 5 years of life. However, the results mainly came from those in the age group of 2 to 5 years instead of the first 2 years in their lives. [ABSTRACT FROM AUTHOR]