Sigma Partitioning: Complexity and Random Graphs

A $\textit{sigma partitioning}$ of a graph $G$ is a partition of the vertices into sets $P_1, \ldots, P_k$ such that for every two adjacent vertices $u$ and $v$ there is an index $i$ such that $u$ and $v$ have different numbers of neighbors in $P_i$. The $\textit{ sigma number}$ of a graph $G$, denoted by $\sigma(G)$, is the minimum number $k$ such that $G$ has a sigma partitioning $P_1, \ldots, P_k$. Also, a $\textit{ lucky labeling}$ of a graph $G$ is a function $\ell :V(G) \rightarrow \mathbb{N}$, such that for every two adjacent vertices $v$ and $u$ of $G$, $\sum_{w \sim v}\ell(w)\neq \sum_{w \sim u}\ell(w)$ ($x \sim y$ means that $x$ and $y$ are adjacent). The $\textit{ lucky number}$ of $G$, denoted by $\eta(G)$, is the minimum number $k$ such that $G$ has a lucky labeling $\ell :V(G) \rightarrow \mathbb{N}_k$. It was conjectured in [Inform. Process. Lett., 112(4):109--112, 2012] that it is $\mathbf{NP}$-complete to decide whether $\eta(G)=2$ for a given 3-regular graph $G$. In this work, we prove this conjecture. Among other results, we give an upper bound of five for the sigma number of a uniformly random graph

A Combined Fuzzy Logic and Analytical Hierarchy Process Method for Optimal Selection and Locating of Pedestrian Crosswalks

One of the main challenges for transportation engineers is the consideration of pedestrian safety as the most vulnerable aspect of the transport system. In many countries around the world, a large number of accidents recorded by the police are composed of accidents involving pedestrians and vehicles, for example when pedestrians may be struck by passing vehicles when crossing the street. Careful consideration of the parameters that are involved in selecting the type and optimum location of pedestrian crosswalks results in a higher pedestrian safety coefficient and a reduced accident rate at these facilities. At the start of this study, these parameters that are important in specifying the optimum type and location of pedestrian crosswalks were determined. Then the data layers of these identified parameters were defined using the ArcGIS software. These layers can subsequently be used for determination of the optimal positioning of pedestrian crosswalks. To specify the boundary changes for each parameter, fuzzy membership functions were defined for each parameter using fuzzy logic. The Analytical Hierarchy Process method (AHP) was used in order to combine these layers of information after the fuzzy membership functions were defined. Expert Choice software was used to determine the final weight resultant of the professionals' poll that was conducted. A field study sample has been carried out to determine the optimal location of pedestrian crosswalks in the city of Tehran. The final output from the ArcGIS software shows the ideal locations and the appropriate type of pedestrian crosswalks in the field study sample. The results indicate that the use of fuzzy logic in definition of membership functions of location parameters, along with using AHP for determination of the weight of data layers built in ArcGIS, is a satisfactory combined method for specifying the location of pedestrian crosswalks

Evaluation of the correlation between serum lipid characteristics of obese subjects and ADIPOQ gene rs266729 polymorphism in Chaharmahal and Bakhtiari Province of Iran

Obesity is a multifactorial disorder that is influenced by various factors such as behavior, diet, environment, metabolic and genetic. This disease is the result of an imbalance between energy absorption and expenditure. Mutations in genes that are responsible for appetite control and metabolism are considered as the genetic component of obesity. Adiponectin protein is one of the most effective adipokines in regulating the body's energy homeostasis and fat storage, which is expressed by the ADIPOQ gene and secreted from white adipose tissue. The concentration of this protein in the blood decreases in obesity. In this study, the relationship between rs266729 polymorphism in the ADIPOQ gene with the level of biochemical parameters such as total cholesterol and triglyceride and HDL and LDL in the blood of obese people in Borujen (a city in Iran) was investigated. This study was performed on 100 people who referred to the Tamin Ejtemaee clinic due to obesity problems in Borujen. In this study, the ARMS-PCR method was used to determine the genotype of individuals. Based on the results of this study, no significant relationship was found between biochemical parameters including total cholesterol, triglyceride, and LDL with rs266729 polymorphism genotypes in ADIPOQ gene in obese subjects. We concluded that rs266729 polymorphism cannot be useful as an index parameter for predispose genotype for imbalance in total cholesterol, triglyceride, and LDL levels in a person

The Effect of Silicone Oil and Nano-hydroxyapatite/Chitosan Powder on Microhardness and Surface Structure of Primary Teeth Enamel After Iron Drop Consumption

Objective: Oral iron drops are recommended for children aged 6-24 months to prevent iron- deficiency anemia. However, their use is associated with the potential risk of erosion and microhardness reduction of primary teeth enamel due to their high acidity. It seems that the combination of silicone oil, nano-hydroxyapatite and chitosan powder may be able to improve the microhardness and surface structure of primary teeth enamel. This study sought to assess the effect of silicone oil plus nano-hydroxyapatite/chitosan on the changed microhardness and surface  structure of primary teeth enamel after exposure to iron drop.Methods: In this in-vitro study, 30 anterior deciduous teeth were collected and randomly divided  into 3 groups. In the first group, samples were exposed to iron drop for 5min and then treated with nano-hydroxyapatite/chitosan and silicone oil for 10min. In the second group, specimens were first treated with the mentioned compound and then exposed to iron drop. Microhardness changes were compared in each group using Wilcoxon one sample or Sign test and between the two groups using Mann Whitney U test. The third group specimens were observed with a scanning electron microscope (SEM) to assess their surface texture and quality.Results: In the first group, iron drop exposure decreased enamel microhardness by 44% of the baseline value (p<0.001). Application of the understudy compound after iron drop exposure significantly increased enamel microhardness by 3% of the baseline value (p=0.006). Use of the mentioned compound before iron drop exposure significantly increased enamel microhardness by  2% of the baseline value (p=0.023). No statistically significant difference was found between the  two groups (p=0.74).Conclusion: Iron drop exposure significantly decreased enamel microhardness. Use of silicone oil and nano-hydroxyapatite/chitosan powder caused 3% and 2% increase in enamel microhardness in the first and 2nd group, respectively. These values, compared to the effect of iron drop exposure are clinically significant

Construction of single domain camel antibody library against breast cancer cellular antigens

زمینه و هدف: آنتی بادی های زنجیره سنگین شتری Camelied-derived heavy chain) (VHH= یک آنتی بادی شتری بوده و کوچک ترین واحد باند شونده به آنتی ژن است. اندازه کوچک نانوبادی ها بزرگ ترین مزیت آن ها می باشد که سبب دستکاری ژنتیکی راحت آن ها می شود. این مطالعه با هدف ساخت کتابخانه ی آنتی بادی تک دمین از شتر ایمن شده با یک رده سلولی آدنوکارسینومای سینه ی انسان (SKBR3) طراحی و اجرا شد. روش بررسی: در این مطالعه تجربی ابتدا عصاره سلول SKBR3 طی سه نوبت به صورت زیر پوستی به یک شتر تزریق گردید. سپس RNA کامل از طحال شتر استخراج و قطعات VHH به کمک روش RT-PCR ساخته و تکثیر شدند. قطعات VHH در درون فاژمید Pcomb3x قرار گرفتند و به روش الکتروپوریشن قطعات نوترکیب وارد باکتری های DH5α شدند. تنوع کتابخانه ی تهیه شده توسط تکنیک انگشت نگاری آنزیمی مورد بررسی قرار گرفت و در نهایت بیان VHH با روش SDS-PAGE ارزیابی شد. یافته ها: در این پژوهش کتابخانه آنتی بادی شتری با بیش از 105 کلونی ساخته شد. همچنین انگشت نگاری آنزیمی نشان داد که کتابخانه ی آنتی بادی حاصل دارای تنوع بالایی می باشد. بررسی های اولیه بوسیله SDS-PAGE مشخص کرد که پروتئین VHH با وزن مولکولی 15 کیلو دالتون در باکتری های ترانسفورم شده بیان می شود. نتیجه گیری: تهیه ی کتابخانه ی آنتی بادی ایمن بر ضد رده سلولی SKBR3، امکان جداسازی آنتی بادی های اختصاصی VHH بر ضد آنتی ژن های مختلف سرطان سینه را فراهم می کند

Five-year Survival Rate of Prostate Cancer in Iran: Results of the national cancer-registry system during 2010-2015

Background: Prostate Cancer is recognized as the second cause of death due to cancers among men worldwide. Due to the lack of local evidence on the survival rate of patients with prostate cancer, this study aimed to estimate the 5-year survival rate of patients afflicted with this condition in Iran. Materials and Methods:  This study made use of information on 9,772 prostate cancer cases who were registered in the National Cancer Registry during 2010-15. A telephone survey, with a response rate of 35%, was conducted to gather additional information such as death status, demographic characteristics, and clinical profile. Kaplan-Meier estimates was used to estimate five-year survival rates. Results: The overall five-year survival rate of prostate cancer was 82% (95% CI: 80-83%).  Significantly higher five-year survival rates were observed among retired patients (rate: 94%,95%CI: 92-96), patients receiving a combination of radiotherapy and surgery (rate: 92%,95%CI: 89-94), and patients residing in rural areas (rate: 92%, 95%CI: 90-93). Conclusion: We found that various factors such as occupation, area of residence, and the type of medication, may influence on survival rate of prostate cancer. Careful evaluation and understanding of effective factors are required to adopt proper health policies and treatment options. Due to the importance of etiologic and epidemiological data, inclusion of such data into the national registry system for Prostate Cancer is strongly recommended

Effect of selenium supplementation with sodium selenite and selenium nanoparticles on iron homeostasis and transferrin gene expression in sheep: A preliminary study

The present research aimed at evaluating the effects of sodium selenite and selenium nanoparticles (Se NPs) on iron homeostasis and the expression of transferrin and its receptor-binding protein genes. Twenty one Lori–Bakhtiary sheep were randomly allocated into 3 groups. Groups 1 and 2 orally received Se NPs and sodium selenite (1 mg kg�1) for 10 consecutive days, respectively. Group 3 served as the control. Blood and sternal bone marrow samples were collected at different supplementation intervals. Various factors such as serum iron concentration, total iron binding capacity (TIBC), and transferrin saturation percent were determined. The expression of transferrin and transferrin binding receptor genes was also studied. Results showed a decreasing trend in serum iron concentration particularly during the early and middle stages of supplementation (0–20 days) with Se NPs or selenium ions. Conversely, the TIBC level increased in sera especially during these periods (0–20 days) in animals that received selenium NPs or selenium ions. Our results also showed that expression of transferrin and its receptor genes was considerably increased during supplementation of the animals by both selenium compounds for 10 or 20 days. After this period, the expression of the mentioned genes significantly decreased, especially in animals that received selenium ions