On the expected diameter, width, and complexity of a stochastic convex-hull

We investigate several computational problems related to the stochastic convex hull (SCH). Given a stochastic dataset consisting of $n$ points in $\mathbb{R}^d$ each of which has an existence probability, a SCH refers to the convex hull of a realization of the dataset, i.e., a random sample including each point with its existence probability. We are interested in computing certain expected statistics of a SCH, including diameter, width, and combinatorial complexity. For diameter, we establish the first deterministic 1.633-approximation algorithm with a time complexity polynomial in both $n$ and $d$. For width, two approximation algorithms are provided: a deterministic $O(1)$-approximation running in $O(n^{d+1} \log n)$ time, and a fully polynomial-time randomized approximation scheme (FPRAS). For combinatorial complexity, we propose an exact $O(n^d)$-time algorithm. Our solutions exploit many geometric insights in Euclidean space, some of which might be of independent interest

Collaboration in Social Networks

The very notion of social network implies that linked individuals interact repeatedly with each other. This allows them not only to learn successful strategies and adapt to them, but also to condition their own behavior on the behavior of others, in a strategic forward looking manner. Game theory of repeated games shows that these circumstances are conducive to the emergence of collaboration in simple games of two players. We investigate the extension of this concept to the case where players are engaged in a local contribution game and show that rationality and credibility of threats identify a class of Nash equilibria -- that we call "collaborative equilibria" -- that have a precise interpretation in terms of sub-graphs of the social network. For large network games, the number of such equilibria is exponentially large in the number of players. When incentives to defect are small, equilibria are supported by local structures whereas when incentives exceed a threshold they acquire a non-local nature, which requires a "critical mass" of more than a given fraction of the players to collaborate. Therefore, when incentives are high, an individual deviation typically causes the collapse of collaboration across the whole system. At the same time, higher incentives to defect typically support equilibria with a higher density of collaborators. The resulting picture conforms with several results in sociology and in the experimental literature on game theory, such as the prevalence of collaboration in denser groups and in the structural hubs of sparse networks

Clinical submission of supernumerary head of adducter brevis muscle

Adductor brevis is an important member of the adductor family occupying the medial compartment of the thigh executing the function of adduction and medial rotation. Deviations from normal anatomy are unusual and rarely reported. A survey of anatomical archives revealed occasional mention of additional bellies of adductor brevis muscle. The present study reports a double belly of adductor brevis muscle (AB) found during a cadaveric dissection class for medical students. The left sided AB displayed two bellies disposed in the same plane. This case report attempts to present the clinical applications of supernumerary bellies of this important adductor muscle of the thigh. It is feasible to categorize these muscular variations upon specialized radiological procedures such as CT and MRI scans only if the radiologist possesses satisfactory understanding of variant anatomy of this region. It is thereafter inferred that upon recognition these muscles present a fair chance of being of utilitised in reconstructions. A biomechanical overview of the present anomaly is also attempte

Preferences for Prenatal Tests for Cystic Fibrosis: A Discrete Choice Experiment to Compare the Views of Adult Patients, Carriers of Cystic Fibrosis and Health Professionals

As new technologies enable the development of non-invasive prenatal diagnosis (NIPD) for cystic fibrosis (CF), research examining stakeholder views is essential for the preparation of implementation strategies. Here, we compare the views of potential service users with those of health professionals who provide counselling for prenatal tests. A questionnaire incorporating a discrete choice experiment examined preferences for key attributes of NIPD and explored views on NIPD for CF. Adult patients (n = 92) and carriers of CF (n = 50) were recruited from one children’s and one adult NHS specialist CF centre. Health professionals (n = 70) were recruited via an e-mail invitation to relevant professional bodies. The key attribute affecting service user testing preferences was no miscarriage risk, while for health professionals, accuracy and early testing were important. The uptake of NIPD by service users was predicted to be high and includes couples that would currently decline invasive testing. Many service users (47%) and health professionals (55.2%) thought the availability of NIPD for CF would increase the pressure to undergo prenatal testing. Most service users (68.5%) thought NIPD for CF should be offered to all pregnant women, whereas more health professionals (68.2%) thought NIPD should be reserved for known carrier couples. The implications for clinical practice are discussed

Improving Students\u27 Vocabulary Mastery by Using Songs at the Grade Sixth of State Elementary School of 45 Bungo Pasang Padang

Kosakata merupakan komponen terpenting dalam menunjang keahlian berbahasa. Namun, Kenyataan di lapangan menunjukkan bahwa siswa/siswi kelas VI SDN. 45 Bungo Pasang Padang kurang menguasai kosakata. Hasil yang didapatkan dari nilai awal siswa/siswi kosakata mereka masih rendah. Hal ini disebabkan dua faktor yaitu kurang motivasi dan teknik yang diajarkan guru. Tujuan penelitian ini adalah untuk mengambarkan dan menjelaskan apakah dengan nyanyian (songs) dalam pengusaan kosakata siswa/siswikelas VI SDN

Implementasi Kebijakan Peran Serta Lingkungan Pendidikan Tinggi Berwawasan Anti Narkoba Di Kota Semarang

Circulation and drug abuse in Indonesia is a multidimensional and multisectoral problem, all lines of life can be exposed to the dangers of drugs. Not apart from that students or young people are the main target of drug abuse, given the level of emotions that have not been stable so easily affected to abuse drugs. Based on Act No 35 of 2009, the Government established the National Narcotics Agency to tackle the drug problem that became a problem in Indonesia, BNN was given the authority of investigation and investigation of narcotics crime and narcotics precursor. In the effort to prevent abuse and illicit drug trafficking as well as handling of government drug problem to include all components of society both from campus environment and work environment. Based on the Regulatory Chief of BNN No 16 of 2014, a Community Participation Container was established to implement the policy towards the participation of the Higher Education Environment. Technical analysis to obtain data through interview with informant, observation, and supporting document. This research uses Merilee S. Grindle theory which argues that the driving factors of implementation have three main factors, namely policy content and policy environment, then the implementation result can be seen from the impact and change on society. The results of this study indicate that the Implementation of the Policy of the Role of the Environment of Higher Education with Anti-Drugs is quite successful in reducing the number of abuse in Semarang City, but still less than optimal with the decrease of performance, and the level of service provided, resulting in the decreasing interest of the Students to join the Unit Anti-drug duties. The desired changes to the creation of an Anti-Narcotics Based Higher Education Environment. The recommendations are to improve the performance and quality of training and counseling, innovation in order to provide facilities and infrastructure that are in line with community expectations

Precise time and frequency intercomparison between NPL, India and PTB, Federal Republic of Germany via satellite symphonie-1

A time and frequency intercomparison experiment conducted using Earth stations in New Delhi, India and Raisting, FRG is described. The NPL clock was placed at New Delhi Earth Station and the Raisting Clock was calibrated with PTB/Primary standard via LORAN-C and travelling clocks. The random uncertainity of time comparisons, represented by two sample Allan Variance sigma (30 seconds), was less than 10 nanoseconds. The relative frequency difference between the NPL and Raisting Clocks, SNPL, RAIS, as measured over the 44 days period was found to be -15.7 x 10 to the -13th power. The relative frequency difference between PTB Primary Standard and Raisting Clock, SPTB, RAIS, during this period, was measured to be -22.8 x 10 to the -13th power. The relative frequency difference between NPL clock and PTB Primary Standard, SNPL, PTB, thus, is +7.1 x 10 to the -13th power. The clock rate (UTC, India) of +7.1 + or - 0.5 x 10 to the -13th power, agrees well with that obtained via VLF phase measurements over one year period and with USNO travelling clock time comparisons made in September, 1980

X-ray Diffraction Analysis of Severely Cold Deformed Hypereutectoid Steel Wire

Hypereutectoid steel wire rod of diameter 6.40 mm is lead patented in lead bath of an electric powered furnace and then it is cold drawn through converging conical dies in a die sequence up to 2.50 mm diameter. The drawn wires subjected to different true strain are analysed using line profile X-ray diffraction methods. The classical Williamson-Hall plot as well as modified Williamson-Hall plot of drawn wire specimens of different true strain is plotted. The theoretical as well as experimental value of q is evaluated. The q is a parameter which depends up on elastic constant of the crystal and type of dislocations. The changes in nature of dislocations from edge dislocations to screw dislocations are calculated against true strain and are verified by scanned electron microscopy’s micrograph of drawn wire