Fourier sparsity, spectral norm, and the Log-rank conjecture

We study Boolean functions with sparse Fourier coefficients or small spectral norm, and show their applications to the Log-rank Conjecture for XOR functions f(x\oplus y) --- a fairly large class of functions including well studied ones such as Equality and Hamming Distance. The rank of the communication matrix M_f for such functions is exactly the Fourier sparsity of f. Let d be the F2-degree of f and D^CC(f) stand for the deterministic communication complexity for f(x\oplus y). We show that 1. D^CC(f) = O(2^{d^2/2} log^{d-2} ||\hat f||_1). In particular, the Log-rank conjecture holds for XOR functions with constant F2-degree. 2. D^CC(f) = O(d ||\hat f||_1) = O(\sqrt{rank(M_f)}\logrank(M_f)). We obtain our results through a degree-reduction protocol based on a variant of polynomial rank, and actually conjecture that its communication cost is already \log^{O(1)}rank(M_f). The above bounds also hold for the parity decision tree complexity of f, a measure that is no less than the communication complexity (up to a factor of 2). Along the way we also show several structural results about Boolean functions with small F2-degree or small spectral norm, which could be of independent interest. For functions f with constant F2-degree: 1) f can be written as the summation of quasi-polynomially many indicator functions of subspaces with \pm-signs, improving the previous doubly exponential upper bound by Green and Sanders; 2) being sparse in Fourier domain is polynomially equivalent to having a small parity decision tree complexity; 3) f depends only on polylog||\hat f||_1 linear functions of input variables. For functions f with small spectral norm: 1) there is an affine subspace with co-dimension O(||\hat f||_1) on which f is a constant; 2) there is a parity decision tree with depth O(||\hat f||_1 log ||\hat f||_0).Comment: v2: Corollary 31 of v1 removed because of a bug in the proof. (Other results not affected.

Epidemiological determinants of spread of causal agent of severe acute respiratory syndrome in Hong Kong.

BACKGROUND: Health authorities worldwide, especially in the Asia Pacific region, are seeking effective public-health interventions in the continuing epidemic of severe acute respiratory syndrome (SARS). We assessed the epidemiology of SARS in Hong Kong. METHODS: We included 1425 cases reported up to April 28, 2003. An integrated database was constructed from several sources containing information on epidemiological, demographic, and clinical variables. We estimated the key epidemiological distributions: infection to onset, onset to admission, admission to death, and admission to discharge. We measured associations between the estimated case fatality rate and patients' age and the time from onset to admission. FINDINGS: After the initial phase of exponential growth, the rate of confirmed cases fell to less than 20 per day by April 28. Public-health interventions included encouragement to report to hospital rapidly after the onset of clinical symptoms, contact tracing for confirmed and suspected cases, and quarantining, monitoring, and restricting the travel of contacts. The mean incubation period of the disease is estimated to be 6.4 days (95% CI 5.2-7.7). The mean time from onset of clinical symptoms to admission to hospital varied between 3 and 5 days, with longer times earlier in the epidemic. The estimated case fatality rate was 13.2% (9.8-16.8) for patients younger than 60 years and 43.3% (35.2-52.4) for patients aged 60 years or older assuming a parametric gamma distribution. A non-parametric method yielded estimates of 6.8% (4.0-9.6) and 55.0% (45.3-64.7), respectively. Case clusters have played an important part in the course of the epidemic. INTERPRETATION: Patients' age was strongly associated with outcome. The time between onset of symptoms and admission to hospital did not alter outcome, but shorter intervals will be important to the wider population by restricting the infectious period before patients are placed in quarantine

Transmission dynamics of the etiological agent of SARS in Hong Kong: impact of public health interventions.

We present an analysis of the first 10 weeks of the severe acute respiratory syndrome (SARS) epidemic in Hong Kong. The epidemic to date has been characterized by two large clusters-initiated by two separate "super-spread" events (SSEs)-and by ongoing community transmission. By fitting a stochastic model to data on 1512 cases, including these clusters, we show that the etiological agent of SARS is moderately transmissible. Excluding SSEs, we estimate that 2.7 secondary infections were generated per case on average at the start of the epidemic, with a substantial contribution from hospital transmission. Transmission rates fell during the epidemic, primarily as a result of reductions in population contact rates and improved hospital infection control, but also because of more rapid hospital attendance by symptomatic individuals. As a result, the epidemic is now in decline, although continued vigilance is necessary for this to be maintained. Restrictions on longer range population movement are shown to be a potentially useful additional control measure in some contexts. We estimate that most currently infected persons are now hospitalized, which highlights the importance of control of nosocomial transmission

SARS-CoV Antibody Prevalence in All Hong Kong Patient Contacts

A total of 1,068 asymptomatic close contacts of patients with severe acute respiratory (SARS) from the 2003 epidemic in Hong Kong were serologically tested, and 2 (0.19%) were positive for SARS coronavirus immunoglobulin G antibody. SARS rarely manifests as a subclinical infection, and at present, wild animal species are the only important natural reservoirs of the virus

Does economic development contribute to sex differences in ischaemic heart disease mortality? Hong Kong as a natural experiment using a case-control study

<p>Abstract</p> <p>Background</p> <p>The male excess risk of premature ischemic heart disease (IHD) mortality may be partially due to an unknown macro-environmental influence associated with economic development. We examined whether excess male risk of IHD mortality was higher with birth in an economically developed environment.</p> <p>Methods</p> <p>We used multivariable logistic regression in a population-based case-control study of all adult deaths in Hong Kong Chinese in 1998 to compare sex differences in IHD mortality (1,189 deaths in men, 1,035 deaths in women and 20,842 controls) between Hong Kong residents born in economically developed Hong Kong or in contemporaneously undeveloped Guangdong province in China.</p> <p>Results</p> <p>Younger (35–64 years) native-born Hong Kong men had a higher risk of IHD death than such women (odds ratio 2.91, 95% confidence interval 1.66 to 5.13), adjusted for age, socio-economic status and lifestyle. There was no such sex difference in Hong Kong residents who had migrated from Guangdong. There were no sex differences in pneumonia deaths by birth place.</p> <p>Conclusion</p> <p>Most of these people migrated as young adults; we speculate that environmentally mediated differences in pubertal maturation (when the male disadvantage in lipids and fat patterning emerges) may contribute to excess male premature IHD mortality in developed environments.</p

The epidemiology of severe acute respiratory syndrome in the 2003 Hong Kong epidemic: an analysis of all 1755 patients.

BACKGROUND: As yet, no one has written a comprehensive epidemiologic account of a severe acute respiratory syndrome (SARS) outbreak from an affected country. OBJECTIVE: To provide a comprehensive epidemiologic account of a SARS outbreak from an affected territory. DESIGN: Epidemiologic analysis. SETTING: The 2003 Hong Kong SARS outbreak. PARTICIPANTS: All 1755 cases and 302 deaths. MEASUREMENTS: Sociodemographic characteristics; infection clusters by time, occupation, setting, and workplace; and geospatial relationships were determined. The mean and variance in the time from infection to onset (incubation period) were estimated in a small group of patients with known exposure. The mean and variance in time from onset to admission, from admission to discharge, or from admission to death were calculated. Logistic regression was used to identify important predictors of case fatality. RESULTS: 49.3% of patients were infected in clinics, hospitals, or elderly or nursing homes, and the Amoy Gardens cluster accounted for 18.8% of cases. The ratio of women to men among infected individuals was 5:4. Health care workers accounted for 23.1% of all reported cases. The estimated mean incubation period was 4.6 days (95% CI, 3.8 to 5.8 days). Mean time from symptom onset to hospitalization varied between 2 and 8 days, decreasing over the course of the epidemic. Mean time from onset to death was 23.7 days (CI, 22.0 to 25.3 days), and mean time from onset to discharge was 26.5 days (CI, 25.8 to 27.2 days). Increasing age, male sex, atypical presenting symptoms, presence of comorbid conditions, and high lactate dehydrogenase level on admission were associated with a greater risk for death. LIMITATIONS: Estimates of the incubation period relied on statistical assumptions because few patients had known exposure times. Temporal changes in case management as the epidemic progressed, unavailable treatment information, and several potentially important factors that could not be thoroughly analyzed because of the limited sample size complicate interpretation of factors related to case fatality. CONCLUSIONS: This analysis of the complete data on the 2003 SARS epidemic in Hong Kong has revealed key epidemiologic features of the epidemic as it evolved

The effect of brief counselling and NRT sampling on the recruitment of smokers to quit smoking

Introduction The smoking population has declined to 10.8% in Hong Kong in 2017 thematic household survey. The passive recruitment measures to motivated smokers to join smoking cessation service exclusively results in a significant missed opportunity to capture the remaining majority of smokers who are not yet planning quit attempts. 2012 Cochrane review suggests that proactive personal contact with potential participants and tailored intervention may help to recruit smokers into smoking cessation programme. The majority of smokers are ambivalent about quitting. Emerging evidence reveals that providing NRT samples engage both motivated and unmotivated smokers into the quitting process. Methodology In the past two years, a mobile truck was deployed to park at different smoking hotspots to reach the smoking population. We provide brief counselling using 5 A’s and 5 R’ techniques to engage the smokers. Free one week nicotine replacement therapy (NRT), either patch or gum was provided for those who were aged 18 or above, no chronic medical diseases or mental illness, not pregnant or breast feeding no recent hospital admission in the recent 6 months and no contraindications on the use of NRT. They were then recommended to join our formal smoking cessation programme. Phone follow up were arranged within one week to answer queries on any side effects. Those not eligible for NRT sample were also encouraged to join our service. Personal data were collected. Number of smokers who had received NRT sample and those who had enrolled our full treatment programme were recorded. The self-reported 7-day point prevalence abstinence rate at 8th and 26th week were ascertained by phone contact. Those who defaulted or could not be contacted were considered failure to quit by intention to treat analysis. Results 2,890 smokers were engaged with brief counseling and 1,394 (48.24%) enrolled our smoke cessation programme The mean age was 41.68 (SD 13.24) with male 2,324 (81.29%) and female 536 (18.71%) with 30 missing data on gender. The average cigarette consumption per day was 17.29 (SD 8.46). The average Fagerstrom score was 4.74 (SD2.38). 1,842(63.74%) received sample NRT of whom 810 (810/1842, 44%) enrolled our full treatment programme whereas 584 (584/1048, 55.7%) without NRT sample enrolled our service. The 7-day point prevalence abstinence rate of all the enrollees at 8th week, 26th week were 47.34%, 38.85% respectively. There was no major adverse events reported. Discussion and Conclusion Many smokers are in a state of contemplation or have no intention of quitting. Our initiative successfully induced 48.2% smokers to undergo formal smoking cessation treatment. The self-reported 7-day point prevalence abstinence rate at 8th and 26th was satisfactory