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.

Fostering equitable access to higher education in Hong Kong : a study of the tertiary financial assistance scheme

published_or_final_versionPolitics and Public AdministrationMasterMaster of Public Administratio

Sulfonylurea is associated with higher risks of ventricular arrhythmia or sudden cardiac death compared with metformin: A population-based cohort study

Background Commonly prescribed diabetic medications such as metformin and sulfonylurea may be associated with different arrhythmogenic risks. This study compared the risk of ventricular arrhythmia or sudden cardiac death between metformin and sulfonylurea users in patients with type 2 diabetes. Methods and Results Patients aged ≥40 years who were diagnosed with type 2 diabetes or prescribed antidiabetic agents in Hong Kong between January 1, 2009, and December 31, 2009, were included and followed up until December 31, 2019. Patients prescribed with both metformin and sulfonylurea or had prior myocardial infarction were excluded. The study outcome was a composite of ventricular arrhythmia or sudden cardiac death. Metformin users and sulfonylurea users were matched at a 1:1 ratio by propensity score matching. The matched cohort consisted of 16 596 metformin users (47.70% men; age, 68±11 years; mean follow‐up, 4.92±2.55 years) and 16 596 sulfonylurea users (49.80% men; age, 70±11 years; mean follow‐up, 4.93±2.55 years). Sulfonylurea was associated with higher risk of ventricular arrhythmia or sudden cardiac death than metformin hazard ratio (HR, 1.90 [95% CI, 1.73–2.08]). Such difference was consistently observed in subgroup analyses stratifying for insulin usage or known coronary heart disease. Conclusions Sulfonylurea use is associated with higher risk of ventricular arrhythmia or sudden cardiac death than metformin in patients with type 2 diabetes

Effectiveness of BNT162b2 and CoronaVac vaccinations against mortality and severe complications after SARS-CoV-2 Omicron BA.2 infection: a case–control study

Data regarding protection against mortality and severe complications after Omicron BA.2 infection with CoronaVac and BNT162b2 vaccines remains limited. We conducted a case–control study to evaluate the risk of severe complications and mortality following 1–3 doses of CoronaVac and BNT162b2 using electronic health records database. Cases were adults with their first COVID-19-related mortality or severe complications between 1 January and 31 March 2022, matched with up-to 10 controls by age, sex, index date, and Charlson Comorbidity Index. Vaccine effectiveness against COVID-19-related mortality and severe complications by type and number of doses was estimated using conditional logistic regression adjusted for comorbidities and medications. Vaccine effectiveness (95% CI) against COVID-19-related mortality after two doses of BNT162b2 and CoronaVac were 90.7% (88.6–92.3) and 74.8% (72.5–76.9) in those aged ≥65, 87.6% (81.4–91.8) and 80.7% (72.8–86.3) in those aged 50–64, 86.6% (71.0–93.8) and 82.7% (56.5–93.1) in those aged 18–50. Vaccine effectiveness against severe complications after two doses of BNT162b2 and CoronaVac were 82.1% (74.6–87.3) and 58.9% (50.3–66.1) in those aged ≥65, 83.0% (69.6–90.5) and 67.1% (47.1–79.6) in those aged 50–64, 78.3% (60.8–88.0) and 77.8% (49.6–90.2) in those aged 18–50. Further risk reduction with the third dose was observed especially in those aged ≥65 years, with vaccine effectiveness of 98.0% (96.5–98.9) for BNT162b2 and 95.5% (93.7–96.8) for CoronaVac against mortality, 90.8% (83.4–94.9) and 88.0% (80.8–92.5) against severe complications. Both CoronaVac and BNT162b2 vaccination were effective against COVID-19-related mortality and severe complications amidst the Omicron BA.2 pandemic, and risks decreased further with the third dose

Sleep problems in children with autism spectrum disorder in Hong Kong: a cross-sectional study

BackgroundAutism spectrum disorder (ASD) is a neurodevelopmental disorder with a growing prevalence of sleep problems associated with significant behavioral problems and more severe autism clinical presentation. Little is known about the relationships between autism traits and sleep problems in Hong Kong. Therefore, this study aimed to examine whether children with autism have increased sleep problems than non-autistic children in Hong Kong. The secondary objective was to examine the factors associated with sleep problems in an autism clinical sample.MethodsThis cross-sectional study recruited 135 children with autism and 102 with the same age range of non-autistic children, aged between 6 and 12 years. Both groups were screened and compared on their sleep behaviors using the Children's Sleep Habits Questionnaire (CSHQ).ResultsChildren with autism had significantly more sleep problems than non-autistic children [t(226.73) = 6.20, p < 0.001]. Bed -sharing [beta = 0.25, t(165) = 2.75, p = 0.07] and maternal age at birth [beta = 0.15, t(165) = 2.05, p = 0.043] were significant factors associated with CSHQ score on the top of autism traits. Stepwise linear regression modeling identified that only separation anxiety disorder (beta = 4.83, t = 2.40, p = 0.019) best-predicted CSHQ.ConclusionIn summary, autistic children suffered from significantly more sleep problems and co-occurring separation anxiety disorder brings greater sleep problems as compared to non-autistic children. Clinicians should be more aware of sleep problems to provide more effective treatments to children with autism

Towards a global partnership model in interprofessional education for cross-sector problem-solving

Objectives A partnership model in interprofessional education (IPE) is important in promoting a sense of global citizenship while preparing students for cross-sector problem-solving. However, the literature remains scant in providing useful guidance for the development of an IPE programme co-implemented by external partners. In this pioneering study, we describe the processes of forging global partnerships in co-implementing IPE and evaluate the programme in light of the preliminary data available. Methods This study is generally quantitative. We collected data from a total of 747 health and social care students from four higher education institutions. We utilized a descriptive narrative format and a quantitative design to present our experiences of running IPE with external partners and performed independent t-tests and analysis of variance to examine pretest and posttest mean differences in students’ data. Results We identified factors in establishing a cross-institutional IPE programme. These factors include complementarity of expertise, mutual benefits, internet connectivity, interactivity of design, and time difference. We found significant pretest–posttest differences in students’ readiness for interprofessional learning (teamwork and collaboration, positive professional identity, roles, and responsibilities). We also found a significant decrease in students’ social interaction anxiety after the IPE simulation. Conclusions The narrative of our experiences described in this manuscript could be considered by higher education institutions seeking to forge meaningful external partnerships in their effort to establish interprofessional global health education

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data

Public housing movements in Hong Kong since the seventies: a sociological study

published_or_final_versionHousing ManagementMasterMaster of Housing Managemen