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

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

Design of Simulator to Evaluate Performance Parameters of Scheduling Clouds in Virtual Machine Environment

Cloud computing acts as a vision of infinite computing resources that are provided on-demand to the cloud users as needed and are billed on pay as per usage basis Cloud computing employs the concept of virtualization that provides an opportunity to achieve business and IT objectives Scheduling is one of the most important challenges that a cloud computing environment faces Scheduling process determines the order of execution of jobs and the virtual machine to which job is assigned to execute so as to improve the performance and quality of service and at the same time resources are utilized effectively An attempt has been made in this paper to develop a simulator to schedule a job on allocated virtual machine so as to make efficient resource utilization In the proposed work scheduling is done on the basis of availability of allocated virtual machine providing equal capabilities We assumed that arrival of jobs in a cloud and their execution on a virtual machine is exponentially distributed For analysing the proposed algorithm the performance parameters of scheduling clouds are evaluated in Virtual Machine Environmen

CT attenuation analysis of carotid intraplaque hemorrhage

Background and Purpose: Intraplaque hemorrhage is considered a leading parameter of carotid plaque vulnerability. Our purpose was to assess the CT characteristics of intraplaque hemorrhage with histopathologic correlation to identify features that allow for confirming or ruling out the intraplaque hemorrhage. MATERIALS AND METHODS: This retrospective study included 91 patients (67 men; median age, 657 years; age range, 41-83 years) who underwent CT angiography and carotid endarterectomy from March 2010 to May 2013. Histopathologic analysis was performed for the tissue characterization and identification of intraplaque hemorrhage. Two observers assessed the plaque's attenuation values by using an ROI (≤1 and ≥2 mm2). Receiver operating characteristic curve, Mann-Whitney, and Wilcoxon analyses were performed. RESULTS: A total of 169 slices were assessed (59 intraplaque hemorrhage, 63 lipid-rich necrotic core, and 47 fibrous); the average values of the intraplaque hemorrhage, lipid-rich necrotic core, and fibrous tissue were 17.475 Hounsfield units (HU) and 18.407 HU, 39.476 HU and 48.048 HU, and 91.66 HU and 93.128 HU, respectively, before and after the administration of contrast medium. The Mann-Whitney test showed a statistically significant difference of HU values both in basal and after the administration of contrast material phase. Receiver operating characteristic analysis showed a statistical association between intraplaque hemorrhage and low HU values, and a threshold of 25 HU demonstrated the presence of intraplaque hemorrhage with a sensitivity and specificity of 93.22% and 92.73%, respectively. The Wilcoxon test showed that the attenuation of the plaque before and after administration of contrast material is different (intraplaque hemorrhage, lipid-rich necrotic core, and fibrous tissue had P values of .006, .0001, and .018, respectively). CONCLUSIONS: The results of this preliminary study suggest that CT can be used to identify the presence of intraplaque hemorrhage according to the attenuation. A threshold of 25 HU in the volume acquired after the administration of contrast medium is associated with an optimal sensitivity and specificity. Special care should be given to the correct identification of the ROI