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In the remarkable paper where he proved the equivalence, Kirchberg studied more generally the pairs of C*-algebras(A,B) admitting only one C*-norm on their algebraic tensor product.We call such pairs "nuclear pairs''. A C*-algebra A istraditionally called nuclear if this holds for any C*-algebra B. Our exposition chooses as its cornerstone Kirchberg's theoremasserting the nuclearity of what is for us the "fundamental pair'', namely the pair (B,C)where B is the algebra B of bounded operators on Hilbert space and C isthe full group C*-algebra C of the free group with countably infinitely many generators. Our presentation leads us to highlight two properties of C*-algebras, the Weak Expectation Property (WEP) and the Local Lifting Property (LLP).
One population parameter that is of particular interest to the behavioral scientist is the mean µ of a population. In this chapter, we will discuss two approaches to statistical inference involving the mean of a population: interval estimation and hypothesis testing. Although these approaches are both carried out using samples and they give essentially equivalent results, there is a basic difference between them and it is important to know what this difference is.
In the previous chapter we presented statistical models for answering questions about population means when the design involves either one or two groups and when the population standard deviation is not known. In the case of two groups, we distinguished between paired and independent group designs and presented statistical models tailored to each.
Between 11–13 December 2018, local public health authorities in the West Midlands, England were alerted to 34 reports of diarrhoea with abdominal cramps. Symptom onset was ~10 h after diners ate Christmas meals at a restaurant between 7–9 December 2018. A retrospective case-control study, environmental and microbiological investigations were undertaken to determine the source and control the outbreak. An analytical study was undertaken with odds ratios (OR) and 95% confidence intervals (CI). Forty persons were recruited to the analytical study (28/40 cases). Multivariable analysis found that leeks in cheese sauce was the only item associated with illness (aOR 51.1; 95% CI 4.13–2492.1). Environmental investigations identified significant lapses in food safety, including lapses in temperature control during cooking and hot holding, likely cross-contamination between raw and cooked foods and the reuse of leftover cheese sauce for the next day's service. No food samples were taken during the exposure period. Two faecal samples were positive for Clostridium perfringens with one confirming the enterotoxigenic gene. Cheese sauce is an unusual vehicle for the organism and the first time this has been reported in England.
Here we describe an example of group that is shown using Kazhdan’s property (T) to be such that its full C* algebrafails LLP, although the group is approximately linear (i.e. so-called hyperlinear). Since both amenable and free groups satisfy the latter LLP, it is not easy to produceexamples failing the LLP, and so far this is the only one.
By this time, you, no doubt, have begun to appreciate the important role analytic methods play in the research process by their ability to enable us to uncover the story contained in our data. The overall research process, however, begins not with the analysis of data, but rather with the posing of questions that interest us. It is the questions we ask that motivate us to conduct research, and it is the nature of these questions, from most simple to most challenging, that gives rise to how we design a research study, how we define and measure relevant variables, and how we collect and analyze our data to answer these questions.
In recent years, outbreaks of hand–foot–mouth disease (HFMD) in China, Singapore and other Western Pacific Region, involving millions of children, have become a big threat to public health. This study aimed to quantitatively assess all qualified studies and identify the risk factors for HFMD death. A systematic search of the databases PubMed, Medline, Embase and the Cochrane Library was performed. Study heterogeneity and publication bias were estimated. Seven case–control studies involving 1641 participants (634 died and 1007 survived) were included in the meta-analysis. Human enterovirus 71 infection, male, age ⩽3 years, vomiting, cyanosis, convulsion, duration of fever ⩾3 days, atypical rashes and abdominal distention were not significantly related to HFMD death (P ⩽ 0.05). Lethargy (odds ratio (OR) = 6.62; 95% CI 3.61–12.14; I2 = 0%; P < 0.0001), pneumonoedema/pneumorrhagia (OR = 4.09; 95% CI 2.44–6.87; I2 = 0%; P < 0.0001), seizures (OR = 6.85; 95% CI 2.37–19.74; I2 = 0%; P = 0.0004), dyspnoea (OR = 8.24; 95% CI 2.05–33.19; I2 = 83%; P = 0.003) and coma (OR = 3.76; 95% CI 1.85–7.67; I2 = 0%; P = 0.0003) were significantly associated with HFMD death, which were risk factors for HFMD death.
This is a brief excursion into atopic that belongs to quantum information theory. We prove here that the Connes-Kirchberg problem is equivalent to a question raised by Tsirelson in connection with quantum mechanics. The question involves correlation matrices of various kinds that we discuss using operatorvalued measures in order to highlight the equivalence ofthe Tsirelson problem with the LLP of certain free product C*-algebras.
This chapter discusses the notions of exactness and nuclearity in connection with the completely bounded approximation property (CBAP) and the completely positive approximation property (CPAP).
In our examination of univariate distributions in Chapter 2, three summarizing characteristics of a distribution were discussed. First, its shape (as denoted by its skewness or its symmetry, by how many peaks and/or outliers it has, and so on). Second, its location (as denoted by its middle score, Q). Third, its spread (as denoted by both the range of values and the interquartile range, which is the range of values within which its middle 50 percent falls). In this chapter, we will expand upon that discussion by introducing other summary statistics for characterizing the location, spread, and shape of a distribution.
After the mass campaign of Measles and Rubella vaccination in 2003 in Iran, the cases of measles and rubella infection decreased but still, the cases of rash and fever were reported. It is worth noting that some other viral infections show signs similar to measles and rubella such as some arboviruses. Considering the epidemic outbreak of arbovirus infections in countries neighbouring Iran, we performed this study to estimate the possibility of chikungunya and dengue fever among measles and rubella IgM negative patients presenting with rash and fever from December 2016 to November 2017 in the National Measles Laboratory at Tehran University of Medical Sciences. Serum samples were selected at random from patients from eight provinces. The presence of DENV IgM and CHIKV IgM was examined by enzyme-linked immunosorbent assay. Of the 1306 sera tested, 210 were CHIKV seropositive and 82 were dengue seropositive. Statistical analysis demonstrated a significant increase in the CHIKV IgM antibody seropositivity rate in Kerman (OR = 2.07, 95% CI: 1.10–3.92; P = 0.024) and Fars (OR = 1.77, 95% CI: 1.06–2.93; P = 0.027). The DENV and CHIKV seropositivity rate in summer is higher than in other seasons (P < 0.01). Our seropositive samples suggest possible CHIKV and DENV infection in Iran. It is likely that these viruses are circulating in Iran and there is a need to study vector carriage of these two viruses.
This study documents historical trends of size and political diversity in Americans’ discussion networks, which are often seen as important barometers of social and political health. Contrasting findings from data drawn out of a nationally representative survey experiment of 1,055 Americans during the contentious 2016 U.S. presidential election to data arising from 11 national data sets covering nearly three decades, we find that Americans’ core networks are significantly smaller and more politically homogeneous than at any other period. Several methodological artifacts seem unlikely to account for the effect. We show that in this period, more than before, “important matters” were often framed as political matters, and that this association probably accounts for the smaller networks.
Novel Coronavirus (2019-nCoV [SARS-COV-2]) was detected in humans during the last week of December 2019 at Wuhan city in China, and caused 24 554 cases in 27 countries and territories as of 5 February 2020. The objective of this study was to estimate the risk of transmission of 2019-nCoV through human passenger air flight from four major cities of China (Wuhan, Beijing, Shanghai and Guangzhou) to the passengers' destination countries. We extracted the weekly simulated passengers' end destination data for the period of 1–31 January 2020 from FLIRT, an online air travel dataset that uses information from 800 airlines to show the direct flight and passengers' end destination. We estimated a risk index of 2019-nCoV transmission based on the number of travellers to destination countries, weighted by the number of confirmed cases of the departed city reported by the World Health Organization (WHO). We ranked each country based on the risk index in four quantiles (4th quantile being the highest risk and 1st quantile being the lowest risk). During the period, 388 287 passengers were destined for 1297 airports in 168 countries or territories across the world. The risk index of 2019-nCoV among the countries had a very high correlation with the WHO-reported confirmed cases (0.97). According to our risk score classification, of the countries that reported at least one Coronavirus-infected pneumonia (COVID-19) case as of 5 February 2020, 24 countries were in the 4th quantile of the risk index, two in the 3rd quantile, one in the 2nd quantile and none in the 1st quantile. Outside China, countries with a higher risk of 2019-nCoV transmission are Thailand, Cambodia, Malaysia, Canada and the USA, all of which reported at least one case. In pan-Europe, UK, France, Russia, Germany and Italy; in North America, USA and Canada; in Oceania, Australia had high risk, all of them reported at least one case. In Africa and South America, the risk of transmission is very low with Ethiopia, South Africa, Egypt, Mauritius and Brazil showing a similar risk of transmission compared to the risk of any of the countries where at least one case is detected. The risk of transmission on 31 January 2020 was very high in neighbouring Asian countries, followed by Europe (UK, France, Russia and Germany), Oceania (Australia) and North America (USA and Canada). Increased public health response including early case recognition, isolation of identified case, contract tracing and targeted airport screening, public awareness and vigilance of health workers will help mitigate the force of further spread to naïve countries.
When collecting egocentric network data, visual representations of networks can function as a cognitive aid for depicting relationships, helping to maintain an overview of the relationships, and keeping the attention of the interviewees. Additionally, network maps can serve as a narration generator in qualitative and in mixed-methods studies. While varying visual instruments are used for collecting egocentric network data, little is known about differences among visual tools concerning the influence on the resulting network data, the usability for interviewees, and data validity. The article provides an overview of existing visually oriented tools that are used to collect egocentric networks and discusses their functions, advantages, and limitations. Then, we present results of an experimental study where we compare four different visual tools with regard to networks elicited, manageability, and the impact of follow-up questions. In order to assess the manageability of the four tools, we used the thinking aloud method. The results provide evidence that the decision in favor of a specific visual tool (structured vs. unstructured) can affect the size and composition of the elicited networks. Follow-up questions greatly affect the elicited networks and follow-up cues can level out differences among tools. Respondents tend to prefer the concentric circles tool, with some differences in preferences and manageability of tools between participants with low and those with high socioeconomic status. Finally, assets and drawbacks of the four instruments are discussed with regard to data quality and crucial aspects of the data collection process when using visual tools.
Early changes in biomarker levels probably occur before bloodstream infection (BSI) is diagnosed. However, this issue has not been fully addressed. We aimed at evaluating the kinetics of C-reactive protein (CRP) and plasma albumin (PA) in the 30 days before community-acquired (CA) BSI diagnosis. From a population-based BSI database we identified 658 patients with at least one measurement of CRP or PA from day −30 (D–30) through day −1 (D–1) before the day of CA-BSI (D0) and a measurement of the same biomarker at D0 or D1. Amongst these, 502 had both CRP and PA measurements which fitted these criteria. CRP and PA concentrations began to change inversely some days before CA-BSI diagnosis, CRP increasing by day −3.1 and PA decreasing by day −1.3. From D–30 to D–4, CRP kinetics (expressed as slopes – rate of concentration change per day) was −1.5 mg/l/day. From D–3 to D1, the CRP slope increased to 36.3 mg/l/day. For albumin, the slope between D–30 to D–2 was 0.1 g/l/day and changed to −1.8 g/l/day between D–1 and D1. We showed that biomarker levels begin to change some days before the CA-BSI diagnosis, CRP 3.1 days and PA 1.3 days before.
We describe and analyse an outbreak of measles that affected Belgium early 2017. In total, 289 cases were reported, mostly (53%) in people 15 years or older. For 133 (46%) vaccination status was unknown and a further 117 (41%) were not vaccinated. According to national guidelines, 83 of the unvaccinated cases (29% of total cases) should have received minimum one dose of vaccine, but did not. One in five cases (21%) did not present with the classical triad of fever, rash and any of coryza, conjunctivitis or cough. Rash was the most sensitive symptom, being absent in only six cases. A large proportion of cases (125/289, 43%) required hospitalisation. In hospitalised patients, the most commonly observed complications were hepatic disorders (present in 58/125 hospitalised patients, 46%). Thirty-six of the cases (12%) were in healthcare workers and nosocomial spread contributed importantly to the outbreak. Older age at presentation, altered clinical presentations and presence of complications like hepatitis can delay the correct diagnosis of measles. Clinicians should maintain a high index of suspicion in any individual presenting with rash. If the elimination target is to be reached, catch-up vaccination campaigns should be intensified and target young adults and health care workers.
Tuberculosis (TB) is generally considered a disease that principally afflicts the low-income segments of a population. In the Nanshan District of Shenzhen, China, with the economic transformation and a new Headquarters Economy (HE) emerging, there are now more cases in office workers than in manufacturing workers. To illustrate this trend, we describe a small TB outbreak in an office building located in the centre of the rapidly growing HE district. Two active pulmonary tuberculosis cases were found in workers who shared an office, and whole genome sequencing showed that the genetic distance between the strains of the two cases was just one single nucleotide polymorphism, consistent with intra-office transmission. Investigation of 30 other workers in the same or adjacent offices with interviews, interferon-gamma release assays (IGRAs) and chest X-rays, identified one new TB case and latent tuberculosis infection (LTBI) in 40.0% (12/30) of the contacts. The offices were under-ventilated. None of the IGRA positive, asymptomatic contacts agreed to receive treatment for LTBI, presumably due to TB stigma, and over the next 2 years 69.0% (20/29) of the contacts were lost to follow-up. Treatment for LTBI and stigma of TB remain challenges here. Office workers in the HE of rapidly economic developing areas should be targeted with increased vigilance by TB control programmes.