arXiv subjects

W. K. Wong

Publications and source records attributed to W. K. Wong.

3 recordsLinked to original sources

arXiv2021

SIR Simulation of COVID-19 Pandemic in Malaysia: Will the Vaccination Program be Effective?

Since the end of 2019, COVID-19 has significantly affected the lives of people around the world. Towards the end of 2020, several COVID-19 vaccine candidates with relatively high efficacy have been reported in the final phase of clinical trials. Vaccines have been considered as critical tools for opening up social and economic activities, thereby lessening the impact of this disease on the society. This paper presents a simulation of COVID-19 spread using modified Susceptible-Infected-Removed (SIR) model under vaccine intervention in several localities of Malaysia, i.e. those cities or states with high relatively COVID-19 cases such as Kuala Lumpur, Penang, Sabah, and Sarawak. The results show that at different vaccine efficacy levels (0.75, 0.85, and 0.95), the curves of active infection vary slightly, indicating that vaccines with efficacy above 0.75 would produce the herd immunity required to level the curves. In addition, disparity is significant between implementing or not implementing a vaccination program. Simulation results also show that lowering the reproduction number, R0 is necessary to keep the infection curve flat despite vaccination. This is due to the assumption that vaccination is mostly carried out gradually at the assumed fixed rate. The statement is based on our simulation results with two values of R0: 1.1 and 1.2, indicative of reduction of R0 by social distancing. The lower R0 shows a smaller peak amplitude about half the value simulated with R0=1.2. In conclusion, the simulation model suggests a two-pronged strategy to combat the COVID-19 pandemic in Malaysia: vaccination and compliance with standard operating procedure issued by the World Health Organization (e.g. social distancing).

physics.soc-ph↗

arXiv2011

Asymptotic properties of eigenmatrices of a large sample covariance matrix

Let $S_n=\frac{1}{n}X_nX_n^*$ where $X_n=\{X_{ij}\}$ is a $p\times n$ matrix with i.i.d. complex standardized entries having finite fourth moments. Let $Y_n(\mathbf {t}_1,\mathbf {t}_2,σ)=\sqrt{p}({\mathbf {x}}_n(\mathbf {t}_1)^*(S_n+σI)^{-1}{\mathbf {x}}_n(\mathbf {t}_2)-{\mathbf {x}}_n(\mathbf {t}_1)^*{\mathbf {x}}_n(\mathbf {t}_2)m_n(σ))$ in which $σ>0$ and $m_n(σ)=\int\frac{dF_{y_n}(x)}{x+σ}$ where $F_{y_n}(x)$ is the Marčenko--Pastur law with parameter $y_n=p/n$; which converges to a positive constant as $n\to\infty$, and ${\mathbf {x}}_n(\mathbf {t}_1)$ and ${\mathbf {x}}_n(\mathbf {t}_2)$ are unit vectors in ${\Bbb{C}}^p$, having indices $\mathbf {t}_1$ and $\mathbf {t}_2$, ranging in a compact subset of a finite-dimensional Euclidean space. In this paper, we prove that the sequence $Y_n(\mathbf {t}_1,\mathbf {t}_2,σ)$ converges weakly to a $(2m+1)$-dimensional Gaussian process. This result provides further evidence in support of the conjecture that the distribution of the eigenmatrix of $S_n$ is asymptotically close to that of a Haar-distributed unitary matrix.

math.PR↗

arXiv1997

Critical Points and Phase Transitions in 5D Compactifications of M-Theory

We study critical points of the BPS mass $Z$, the BPS string tension $Z_m$, the black hole potential $V$ and the gauged central charge potential $P$ for M-theory compactified on Calabi-Yau three-folds. We first show that the stabilization equations for $Z$ (determining the black hole entropy) take an extremely simple form in five dimensions as opposed to four dimensions. The stabilization equations for $Z_m$ are also very simple and determine the size of the infinite $adS_3$-throat of the string. The black hole potential in general exhibits two classes of critical points: supersymmetric critical points which coincide with those of the central charge and non-supersymmetric critical points. We then generalize the discussion to the entire extended Kähler cone encompassing topologically different but birationally equivalent Calabi-Yau three-folds that are connected via flop transitions. We examine behavior of the four potentials to probe the nature of these phase transitions. We find that $V$ and $P$ are continuous but not smooth across the flop transition, while $Z$ and its first two derivatives, as well as $Z_m$ and its first derivative, are continuous. This in turn implies that supersymmetric stabilization of $Z$ and $Z_m$ for a given configuration takes place in at most one point throughout the entire extended Kähler cone. The corresponding black holes (or string states) interpolate between different Calabi-Yau three-folds. At the boundaries of the extended Kähler cone we observe that electric states become massless and/or magnetic strings become tensionless.

hep-th↗