Geometric Graph Theory and Wireless Sensor Networks

In this work, we apply geometric and combinatorial methods to explore a variety of problems motivated by wireless sensor networks. Imagine sensors capable of communicating along straight lines except through obstacles like buildings or barriers, such that the communication network topology of the sensors is their visibility graph. Using a standard distributed algorithm, the sensors can build common knowledge of their network topology. We first study the following inverse visibility problem: What positions of sensors and obstacles define the computed visibility graph, with fewest obstacles? This is the problem of finding a minimum obstacle representation of a graph. This minimum number is the obstacle number of the graph. Using tools from extremal graph theory and discrete geometry, we obtain for every constant h that the number of n-vertex graphs that admit representations with h obstacles is 2o(n2). We improve this bound to show that graphs requiring Ω(n / log2 n) obstacles exist. We also study restrictions to convex obstacles, and to obstacles that are line segments. For example, we show that every outerplanar graph admits a representation with five convex obstacles, and that allowing obstacles to intersect sometimes decreases their required number. Finally, we study the corresponding problem for sensors equipped with GPS. Positional information allows sensors to establish common knowledge of their communication network geometry, hence we wish to compute a minimum obstacle representation of a given straight-line graph drawing. We prove that this problem is NP-complete, and provide a O(logOPT)-factor approximation algorithm by showing that the corresponding hypergraph family has bounded Vapnik-Chervonenkis dimension

Clinical characteristics, adjustment between the couples and the quality of sexual life of married women who are exposed to physical domestic violence

Objective: The present study was performed to assess the adjustment between the couples in married women who were exposed to domestic violence and the effects of domestic violence on the quality of sexual life. Method: The study included 162 married women between the ages of 18 and 65 years, who were conse cutively admitted to the general psychiatry outpatient clinic of Ministry of Health Erenköy Research and Education Hospital for Psychiatric and Neurological Diseases between 01.06.2017 and 01.09.2017. Structured psychiatric interview (SCID-I) according to the DSM-IV diagnostic criteria were performed all individuals participating in the study. The patients included in the study completed the sociodemografic data form, domestic violence questionnaire form, Dyadic Adjustment Scale for Measurement of Marital Quality with Turkish Couples and Quality of Sexual Life Questionnaire. Results: Among the patients who participated in the study, 62 (38.27%) of them had been exposed to domestic physical violence. While 42.0% of those who had not been exposed to domestic physical violence had an arranged/involuntary marriage, the percentage of those who had an arranged marriage among women who were exposed to domestic violence was 61.3%. Women who were not exposed to domestic physical violence had significantly higher scores from the Quality of Sexual Life Questionnaire than that of those who were exposed to domestic physical violence (p<0.001). Furthermore, agreement, satisfaction, adjustment and total subscales of the Dyadic Adjustment Scale were found to be signi ficantly higher in women who were not exposed to domestic physical violence (p<0.001). Discussion: We found in the present study that adjustment between the couples and quality of sexual life was quite low in women who were exposed physical domestic violence. It is quite important that people who are dealing with mental health should not only assess the symptoms of the disease but also the components of the woman’s social and cultural background and include domestic violence in the anamnesis

Geometric graph theory and wireless sensor networks

In this work, we apply geometric and combinatorial methods to explore a variety of problems motivated by wireless sensor networks. Imagine sensors capable of communicating along straight lines except through obstacles like buildings or barriers, such that the communication network topology of the sensors is their visibility graph. Using a standard distributed algorithm, the sensors can build common knowledge of their network topology. We first study the following inverse visibility problem: What positions of sensors and obstacles define the computed visibility graph, with fewest obstacles? This is the problem of finding a minimum obstacle representation of a graph. This minimum number is the obstacle number of the graph. Using tools from extremal graph theory and discrete geometry, we obtain for every constant h that the number of n-vertex graphs that admit representations with h obstacles is [special characters omitted]. We improve this bound to show that graphs requiring Ω( n/log2n) obstacles exist. We also study restrictions to convex obstacles, and to obstacles that are line segments. For example, we show that every outerplanar graph admits a representation with five convex obstacles, and that allowing obstacles to intersect sometimes decreases their required number. Finally, we study the corresponding problem for sensors equipped with GPS. Positional information allows sensors to establish common knowledge of their communication network geometry, hence we wish to compute a minimum obstacle representation of a given straight-line graph drawing. We prove that this problem is NP-complete, and provide a O(log OPT)-factor approximation algorithm by showing that the corresponding hypergraph family has bounded Vapnik-Chervonenkis dimension

Synthesis and Characterization of Monoaminophosphine, Bis(Amino) Phosphine Derivatives, and their Metal Complexes

WOS: 000296318500021Functionalized monoaminophosphine of the type Ph2PNR2 (1 and 3) and bis(amino) phosphine of the type PhP(NR2)(2) (2) have been synthesized by treating Ph2PCl or PhPCl2 with corresponding amines. Ligands react with aqueous hydrogen peroxide, elemental sulfur, or selenium to give the corresponding chalcogenides in good yield. The metal complexes of the aminophosphines have been obtained. All of the compounds were obtained in good yields and were characterized by IR, NMR, and microanalysis.Research Foundation of The University of Nigde (NUAF)The authors are grateful to Research Foundation of The University of Nigde (NUAF) for financial support