Dynamic Set Intersection

Consider the problem of maintaining a family $F$ of dynamic sets subject to insertions, deletions, and set-intersection reporting queries: given $S,S'\in F$, report every member of $S\cap S'$ in any order. We show that in the word RAM model, where $w$ is the word size, given a cap $d$ on the maximum size of any set, we can support set intersection queries in $O(\frac{d}{w/\log^2 w})$ expected time, and updates in $O(\log w)$ expected time. Using this algorithm we can list all $t$ triangles of a graph $G=(V,E)$ in $O(m+\frac{m\alpha}{w/\log^2 w} +t)$ expected time, where $m=|E|$ and $\alpha$ is the arboricity of $G$. This improves a 30-year old triangle enumeration algorithm of Chiba and Nishizeki running in $O(m \alpha)$ time. We provide an incremental data structure on $F$ that supports intersection {\em witness} queries, where we only need to find {\em one} $e\in S\cap S'$. Both queries and insertions take O\paren{\sqrt \frac{N}{w/\log^2 w}} expected time, where $N=\sum_{S\in F} |S|$. Finally, we provide time/space tradeoffs for the fully dynamic set intersection reporting problem. Using $M$ words of space, each update costs $O(\sqrt {M \log N})$ expected time, each reporting query costs $O(\frac{N\sqrt{\log N}}{\sqrt M}\sqrt{op+1})$ expected time where $op$ is the size of the output, and each witness query costs $O(\frac{N\sqrt{\log N}}{\sqrt M} + \log N)$ expected time.Comment: Accepted to WADS 201

An update on the management of urinary tract infection

Urinary tract infection (UTI) is commonly encountered in general medical practice. The majority of patients have uncomplicated infections affecting the lower urinary tract, which respond readily to a short course of oral antibiotics. Life-threatening complications or long-term morbidity can occur, especially in patients with underlying medical predispositions or urological abnormalities. Further investigations are warranted in patients with severe or recurrent UTI, or when UTI occurs in 'low risk' individuals. Special investigations to look for vesicoureteric reflux and renal cortical scars should be considered in children with UTI. Screening of pregnant women for asymptomatic UTI is important in view of its propensity to involve the upper urinary tract. A 3-day course of appropriate oral antibiotics is often sufficient for the treatment of uncomplicated lower UTI in young females. A longer treatment duration of up to 7 days may be indicated in elderly subjects. The optimal duration of antibiotic therapy for upper UTI remains controversial. In addition to antibiotic prophylaxis, simple advice on prophylactic measures during activities of daily living is often beneficial to patients with recurrent UTI.published_or_final_versio

Marketized private tutoring as a supplement to regular schooling: Liberal Studies and the shadow sector in Hong Kong secondary education

Around the world, increasing numbers of students receive after-school private supplementary tutoring. Such tutoring may be provided through informal channels or by companies; and it may be received one-to-one, in small groups, or in large classes. The tutoring is commonly called shadow education since its content mimics that of regular schooling. The spread of shadow education is part of a global shift of balance with increased roles for the private sector. Hong Kong is among the societies in which shadow education enrolment rates are particularly high. Much shadow education focuses on techniques for performance in external examinations, and is not consistent with the emphases stressed by teachers and the government. This paper focuses on a newly-introduced subject called Liberal Studies in which the tensions are especially visible. Although the official curriculum emphasizes creativity and critical thinking, many students have sought large-class tutoring focused on formulae for passing examinations. Interviews exposed the needs that the students felt were not being met in their schooling. The findings illustrate some of the complexities in relationships between the public and private sectors. Viewed in a wider context, the paper illuminates some of the mechanisms and effects of marketization which are increasingly evident globally.postprin

Flexural behaviour of stainless steel oval hollow sections

Structural hollow sections are predominantly square, rectangular or circular in profile. While square and circular hollow sections are often the most effective in resisting axial loads, rectangular hollow sections, with greater stiffness about one principal axis than the other, are generally more suitable in bending. Oval or elliptical hollow sections (EHS) combine the aesthetic external profile of circular hollow sections with the suitability for resisting flexure of rectangular sections, whilst also retaining the inherent torsional stiffness offered by all tubular sections. This paper examines the structural response of recently introduced stainless steel oval hollow sections (OHS) in bending and presents design recommendations. In-plane bending tests in the three-point configuration about both the major and minor axes were conducted. All tested specimens were cold-formed from Grade 1.4401 stainless steel and had an aspect ratio of approximately 1.5. The full moment-rotation responses of the specimens were recorded and have been presented herein. The tests were replicated numerically by means of non-linear finite element (FE) analysis and parametric studies were performed to investigate the influence of key parameters, such as the aspect ratio and the cross-section slenderness, on the flexural response. Based on both the experimental and numerical results, structural design recommendations for stainless steel OHS in bending in accordance with Eurocode 3: Part 1.4 have been made

Knuthian Drawings of Series-Parallel Flowcharts

Inspired by a classic paper by Knuth, we revisit the problem of drawing flowcharts of loop-free algorithms, that is, degree-three series-parallel digraphs. Our drawing algorithms show that it is possible to produce Knuthian drawings of degree-three series-parallel digraphs with good aspect ratios and small numbers of edge bends.Comment: Full versio

Simulation of the control method for the adaptive front lighting system

Author name used in this publication: K. W. E. ChengAuthor name used in this publication: S. L. HoVersion of RecordPublishe

Development of electric vehicle with advanced lighting system and all electric drive

Author name used in this publication: K. W. E. ChengAuthor name used in this publication: S. L. HoVersion of RecordPublishe

Colored Non-Crossing Euclidean Steiner Forest

Given a set of $k$-colored points in the plane, we consider the problem of finding $k$ trees such that each tree connects all points of one color class, no two trees cross, and the total edge length of the trees is minimized. For $k=1$, this is the well-known Euclidean Steiner tree problem. For general $k$, a $k\rho$-approximation algorithm is known, where $\rho \le 1.21$ is the Steiner ratio. We present a PTAS for $k=2$, a $(5/3+\varepsilon)$-approximation algorithm for $k=3$, and two approximation algorithms for general~$k$, with ratios $O(\sqrt n \log k)$ and $k+\varepsilon$

Association Patterns of Ontological Features Signify Electronic Health Records in Liver Cancer

published_or_final_versio

Predominant cultivable subgingival flora of renal transplant recipients

postprin