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

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

Smooth Inequalities and Equilibrium Inefficiency in Scheduling Games

We study coordination mechanisms for Scheduling Games (with unrelated machines). In these games, each job represents a player, who needs to choose a machine for its execution, and intends to complete earliest possible. Our goal is to design scheduling policies that always admit a pure Nash equilibrium and guarantee a small price of anarchy for the l_k-norm social cost --- the objective balances overall quality of service and fairness. We consider policies with different amount of knowledge about jobs: non-clairvoyant, strongly-local and local. The analysis relies on the smooth argument together with adequate inequalities, called smooth inequalities. With this unified framework, we are able to prove the following results. First, we study the inefficiency in l_k-norm social costs of a strongly-local policy SPT and a non-clairvoyant policy EQUI. We show that the price of anarchy of policy SPT is O(k). We also prove a lower bound of Omega(k/log k) for all deterministic, non-preemptive, strongly-local and non-waiting policies (non-waiting policies produce schedules without idle times). These results ensure that SPT is close to optimal with respect to the class of l_k-norm social costs. Moreover, we prove that the non-clairvoyant policy EQUI has price of anarchy O(2^k). Second, we consider the makespan (l_infty-norm) social cost by making connection within the l_k-norm functions. We revisit some local policies and provide simpler, unified proofs from the framework's point of view. With the highlight of the approach, we derive a local policy Balance. This policy guarantees a price of anarchy of O(log m), which makes it the currently best known policy among the anonymous local policies that always admit a pure Nash equilibrium.Comment: 25 pages, 1 figur

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

Considerations on the Adoption of Named Data Networking (NDN) in Tactical Environments

Mobile military networks are uniquely challenging to build and maintain, because of their wireless nature and the unfriendliness of the environment, resulting in unreliable and capacity limited performance. Currently, most tactical networks implement TCP/IP, which was designed for fairly stable, infrastructure-based environments, and requires sophisticated and often application-specific extensions to address the challenges of the communication scenario. Information Centric Networking (ICN) is a clean slate networking approach that does not depend on stable connections to retrieve information and naturally provides support for node mobility and delay/disruption tolerant communications - as a result it is particularly interesting for tactical applications. However, despite ICN seems to offer some structural benefits for tactical environments over TCP/IP, a number of challenges including naming, security, performance tuning, etc., still need to be addressed for practical adoption. This document, prepared within NATO IST-161 RTG, evaluates the effectiveness of Named Data Networking (NDN), the de facto standard implementation of ICN, in the context of tactical edge networks and its potential for adoption

A Time-Space Tradeoff for Triangulations of Points in the Plane

In this paper, we consider time-space trade-offs for reporting a triangulation of points in the plane. The goal is to minimize the amount of working space while keeping the total running time small. We present the first multi-pass algorithm on the problem that returns the edges of a triangulation with their adjacency information. This even improves the previously best known random-access algorithm

Heart applications of 4D flow

Four-dimensional (4D) flow sequences are an innovative type of MR sequences based upon phase contrast (PC) sequences which are a type of application of Angio-MRI together with the Time of Flight (TOF) sequences and Contrast-Enhanced Magnetic Resonance Acquisition (CE-MRA). They share the basic principles of PC, but unlike PC sequences, 4D flow has velocity encoding along all three flow directions and three-dimensional (3D) anatomic coverage. They guarantee the analysis of flow with multiplanarity on a post-processing level, which is a unique feature among MR sequences. Furthermore, this technique provides a completely new level to the in vivo flow analysis as it allows measurements in never studied districts such as intracranial applications or some parts of the heart never studied with echo-color-doppler, which is its sonographic equivalent. Furthermore, this technique provides a completely new level to the in vivo flow analysis as it allows accurate measurement of the flows in different districts (e.g., intracranial, cardiac) that are usually studied with echo-color-doppler, which is its sonographic equivalent. Of note, the technique has proved to be affected by less inter and intra-observer variability in several application. 4D-flow basic principles, advantages, limitations, common pitfalls and artefacts are described. This review will outline the basis of the formation of PC image, the construction of a 4D-flow and the huge impact the technique is having on the cardiovascular non-invasive examination. It will be then studied how this technique has had a huge impact on cardiovascular examinations especially on a central heart level

Artificial Intelligence Applications in Cardiovascular Magnetic Resonance Imaging: Are We on the Path to Avoiding the Administration of Contrast Media?

In recent years, cardiovascular imaging examinations have experienced exponential growth due to technological innovation, and this trend is consistent with the most recent chest pain guidelines. Contrast media have a crucial role in cardiovascular magnetic resonance (CMR) imaging, allowing for more precise characterization of different cardiovascular diseases. However, contrast media have contraindications and side effects that limit their clinical application in determinant patients. The application of artificial intelligence (AI)-based techniques to CMR imaging has led to the development of non-contrast models. These AI models utilize non-contrast imaging data, either independently or in combination with clinical and demographic data, as input to generate diagnostic or prognostic algorithms. In this review, we provide an overview of the main concepts pertaining to AI, review the existing literature on non-contrast AI models in CMR, and finally, discuss the strengths and limitations of these AI models and their possible future development

Pulmonary transit time as a marker of diastolic dysfunction in Takotsubo syndrome

AIM: To evaluate the pulmonary transit time (PTT) and its derived parameters using cardiac magnetic resonance imaging (CMRI) as markers of diastolic dysfunction in Takotsubo syndrome (TS) and its relationship with transthoracic echocardiography and CMRI parameters. MATERIALS AND METHODS: Twenty-two patients with TS, who exhibited diastolic dysfunction as assessed by transthoracic echocardiography, were enrolled retrospectively and the PTT, pulmonary transit time index (PTTI), and pulmonary blood volume index (PBVI) were evaluated using first-pass CMRI. PTT was calculated as the number of cardiac cycles required for a bolus of contrast agent to move from the right ventricle (RV) to the left ventricle (LV), whereas PTTI represents the PTT interval corrected for the heart rate. Finally, PBVI was calculated as the product of PTTI, and RV stroke volume indexed for body surface area. Normal references of PTT, PTTI, and PBVI were evaluated in a cohort of 20 age- and sex-matched healthy controls. RESULTS: Compared with healthy subjects, TS patients showed significantly higher PTT, PTTI, and PBVI (p=0.0001, p=0.0001, and p=0.002, respectively). Using multivariable logistic regression, PBVI provided the best differentiation between TS and controls (AUC 0.84). PBVI was significantly associated with the index of diastolic dysfunction and left atrial strain parameters. In addition, PBVI demonstrated a significant correlation with global T2 mapping (r=0,520, p=0,019). CONCLUSION: PTT and the derived parameters, as assessed using first-pass CMRI, are potential tools for assessing LV diastolic dysfunction in patients with TS