https://blog.biocomm.ai/2025/07/31/coherent-and-incoherent-light-scattering-by-single-atom-wave-packets-mit/
https://www.researchgate.net/publication/385292368_Coherent_and_incoherent_light_scattering_by_single-atom_wavepackets
2025年4月9日 星期三
2025升中乙部抽獎形勢
又到乙部派位時間。通常傳媒會用不經大腦的標嚇人。
這個4.6人爭一個英中位是用該網參加抽獎人數去算。
例如中西區就是用
參加抽獎總人數/乙部英中位來算出一個位2個人爭。
但實際上抽獎方法是該網總評分前1/3的學生，即Band 1學生，先派位。
待所有Band 1 生抽完後其他組別才派位。
所以實際上，
中西區band 1 學生每人有1.48個英中位選擇。
灣仔區每人有1.67個位。
九龍城區每人有1.15個位
從下表可見除了上面3個校網及離島網外大部份校網都是約2個band 1生 爭1個英中位。
都是那一句好校網贏在起跑線
2023年12月26日 星期二
從生產力看雅萬高鐵定價—公共財(Public Goods)
雅萬高鐵定價
高鐵二等單程票價20萬印尼盾（USD12.92）。
雅萬巴士單程票價78000盾（USD5.00）。
乘高鐵比巴士多付USD 7.92。-------------------------------------------------------------------（1）
下為印尼部份工種平均月薪：
印尼法例每周工作5天，每天工作8小時，共40小時。1年52周，有工作日260日，
減去
法定假期27日，年假12日，即一年工作（260-27-12）x8小時＝1768小時。
這教師每小時生產力收入 USD 7541.4/1768＝USD 4.265
高鐵全程40分鐘，巴士約3小時。乘高鐵節省2.25小時以上。
節省的時間換算成生產力收入 ：USD 4.265x2.25 ＝USD 9.60 --------------------------------------（2）
這教師乘坐高鐵單程可省下的生產力是：
（2）–（1）
9.60 – 7.92 ＝USD 1.68
換個算法，月薪8,030,000印尼盾以上的人會選擇乘雅萬高鐵來往雅加達—萬隆。
這個票價定價方法與一般的用者自付，自負盈虧的定價方法不同。
基建是公共財(public goods)整條鐵路建設及營運初期會要政府投入資金。
通常是從富裕地區的稅收津貼鐵路。
利用鐵路提升沿途地區發展直至落後地區經濟追上發達地區後就可轉為自負盈虧。
這方法適用於連貫經濟落差大地區的鐵路或收費高速公路。
在發達地區如香港則可利用鐵路站上蓋物業項目收益去支持鐵路建設。
另有中國高鐵定價文章： 高鐵定價與GPA關係
All Rights Reserved©2023 fengshuileung
2023年5月10日 星期三
2023年4月11日 星期二
2022年3月5日 星期六
全民檢測成效成疑，尷尬的數學真相
近日全民檢測新冠病毒甚囂塵上。大部人誤會全民檢測後就可截斷傳播鍊，大家重回正常生活。但從統計學角度這只是一廂情願而已。
下為 EU 對 Rapid Antigen Test 的要求：
[Sensitivity and specificity of nucleic acid testing in close contacts of COVID-19 cases in Guangzhou] 核酸測試靈敏度研究
以下為試劑在不同靈敏度及總體感染量下的估計誤測數及預計隔離人數：
1.
以有感染為陽性。
Sensitivity 90%，即有10%陽性被測不出，被錯認為陰性。Specificity 98%，即有2%陰性被錯認為陽性。
假設本地受感染率為15%，以700萬人計，真陽性應為105萬人。
無感染為595萬人。
陽性但驗不出的有10萬5千人。受感染又驗出陽性的有94萬5千人。
無染疫但卻被劃成陽性的有11萬9千人。
故此陽性準確率是94.5/(94.5+11.9)=88.82%
陰性準確率為583.1/(583.1+10.5)=98.23%
如凡驗出陽性要隔離，則隔離人數為 (94.5+11.9)=106.4萬人。
如只能提供10萬個隔離位則有88.7萬真陽性的人要在家隔離。
另外亦有10.5萬陽性的人走漏進入社區。
2.
以有感染為陽性。
Sensitivity 90%，即有10%陽性被測不出，被錯認為陰性。Specificity 98%，即有2%陰性被錯認為陽性。
假設本地受感染率為10%，以700萬人計，真陽性應為70萬人。
無感染為617.4萬人。
陽性但驗不出的有7萬人。受感染又驗出陽性的有63萬人。
無染疫但卻被劃成陽性的有12萬6千人。
故此陽性準確率是63/(63+12.6)=83.33%
陰性準確率為617.4/(6617.4+7)=98.87%
如凡驗出陽性要隔離，則隔離人數為 (63+12.6)=75.6萬人。
如只能提供10萬個隔離位則有54.7萬真陽性的人要在家隔離。
另外亦有7萬陽性的人走漏進入社區。
3.
以有感染為陽性。
Sensitivity 95%，即有5%陽性被測不出，被錯認為陰性。Specificity 98%，即有2%陰性被錯認為陽性。
假設本地受感染率為10%，以700萬人計，真陽性應為70萬人。
無感染為630萬人。
陽性但驗不出的有3.5萬人。受感染又驗出陽性的有66.5萬人。
無染疫但卻被劃成陽性的有12萬6千人。
故此陽性準確率是66.5/(66.5+12.6)=84.07%
陰性準確率為617.4/(617.4+3.5)=99.44%
如凡驗出陽性要隔離，則隔離人數為 (66.5+12.6)=79.1萬人。
如只能提供10萬個隔離位則有58.1萬真陽性的人要在家隔離。
另外亦有3.5萬陽性的人走漏進入社區。
4.
以有感染為陽性。
Sensitivity 97%，即有3%陽性被測不出，被錯認為陰性。Specificity 98%，即有2%陰性被錯認為陽性。
假設本地受感染率為10%，以700萬人計，真陽性應為70萬人。
無感染為630萬人。
陽性但驗不出的有2.1萬人。受感染又驗出陽性的有67.9萬人。
無染疫但卻被劃成陽性的有12萬6千人。
故此陽性準確率是67.9/(67.9+12.6)=84.35%
陰性準確率為617.4/(617.4+2.1)=99.66%
如凡驗出陽性要隔離，則隔離人數為 (67.9+12.6)=80.5萬人。
如只能提供10萬個隔離位則有59.5萬真陽性的人要在家隔離。
另外亦有2.1萬假陰性真陽性的人走漏進入社區。
5.
以有感染為陽性。（以核酸測試最高 Sensitivity算）
Sensitivity 99%，即有1%陽性被測不出，被錯認為陰性。Specificity 98%，即有2%陰性被錯認為陽性。
假設本地受感染率為10%，以700萬人計，真陽性應為70萬人。
無感染為630萬人。
陽性但驗不出的有0.7萬人。受感染又驗出陽性的有69.3萬人。
無染疫但卻被劃成陽性的有12萬6千人。
故此陽性準確率是69.3/(69.3+12.6)=84.62%
陰性準確率為617.4/(617.4+0.7)=99.89%
如凡驗出陽性要隔離，則隔離人數為 (69.3+12.6)=81.9萬人。
如只能提供10萬個隔離位則有60.84萬真陽性的人要在家隔離。
另外亦有0.7萬假陰性真陽性的人走漏進入社區。
6.
下為最樂觀估計。
目前尚有277萬人一針未打。假定只有一針未打才會染疫。
以有感染為陽性。
Sensitivity 97%，即有3%陽性被測不出，被錯認為陰性。Specificity 98%，即有2%陰性被錯認為陽性。
假設此群組受感染率為15%，以27萬人計，真陽性應為41.55萬人。
無感染為235.45萬人。
陽性但驗不出的有1.25萬人。受感染又驗出陽性的有40.3萬人。
無染疫但卻被劃成陽性的有4萬7千人。
故此陽性準確率是89.54%
陰性準確率為99.46%
如凡驗出陽性要隔離，則隔離人數為 45萬人。
如只能提供10萬個隔離位則有31.35萬真陽性的人要在家隔離。
另外亦有1.25萬假陰性真陽性的人走漏進入社區。
以上只是一次全檢的推算。
要注意的是在家隔離的人因個人及緊密接觸者皆會著重防疫故在轉陰前傳染他人機會是較低。
反為假陰性的數萬人會在正常社交中較大機會傳染他人。
By WK Leung MHKIE, RPE, CEng, MIMarEST, CMarEng
All Rights Reserved©2022 fengshuileung
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其他有關 COVID 19 文章
2021年6月28日 星期一
Triplet control prevents ‘lasing death’ in perovskite lasers
https://physicsworld.com/a/triplet-control-prevents-lasing-death-in-perovskite-lasers/
On paper, perovskites make great building blocks for lasers. In their quasi-two-dimensional form, these organic–inorganic materials exhibit tunable colour and excellent stability. The fact that they can fabricated from low-cost starting components in simple solution-based processes makes them attractive for manufacturers, too. There’s just one tiny flaw: perovskite-based lasers abruptly stop working after only a few minutes of constant operation at room temperature. Now, however, a team of researchers in China and Japan say they have overcome this so-called “lasing death” by suppressing long-lived energetic states known as triplet excitons.
Both 2D and quasi-2D perovskites are promising alternatives to silicon in optoelectronics devices. While 2D perovskites are made up of stacked sheets of alternating organic and inorganic layers, their quasi-2D variants contain small regions in which organic and inorganic materials alternate in all directions (as is the case in their 3D counterparts). The quasi-2D versions also contain two different types of organic materials.
In organic semiconductors such as those that make up quasi-2D perovskites, charge carriers – electrons and holes – come together to form an energetic state called an exciton. This entity may exist in a so-called singlet state (which has no net spin because the contributing electron spins point in opposite directions) or in a triplet state (in which the spins point in the same direction). In both cases, the energy in the exciton can then be released as light via a process known as radiative recombination. Triplets generally have a lower energy than singlets, however, and emit hardly any light.
Long triplet lifetimes
Recently, researchers led by Chuanjiang Qin of the Chinese Academy of Sciences and Chihaya Adachi at Kyushu University in Japan found evidence that triplet excitons have lifetimes of nearly a microsecond in these materials. These long lifetimes led them to focus on these excitons as a possible cause of lasing death.
As well as emitting very little or no light, triplet states also tend to interact with light-emitting singlets in a way that causes both to lose their energy without producing light, Qin explains. Eliminating any triplets in perovskites would therefore prevent interference with lasing.
In their latest work, the researchers studied FAPbBr3-based (where FA is formamidinium) quasi-2D perovskites with two different organic cations, phenylethylammonium bromide (PEABr) and 1-naphthylmethylamine bromide (NMABr). The PEABr-based perovskite contains an organic cation with high triplet energy, and the NMABr-based perovskite has an organic cation with low triplet energy.
Holding triplets in a low energy state
To eliminate triplets in these quasi-2D perovskites, the researchers incorporated an organic layer into the materials, which confines the triplets to a low-energy state. Since the excitons want to move to lower energies, the long-lived triplet excitons transfer from the active (that is, light-emitting) portion of the perovskites to the organic layer, they explain. This reduces light losses and allows for lasing under constant optical excitation (also known as optically pumped continuous-wave, or CW lasing) without interruption.
Qin, Adachi and colleagues also discovered that they could make their material lase continuously simply by placing it in air. This is because oxygen can destroy triplets – a result that further suggests that light losses caused by triplets may indeed be the culprits in lasing death.
Unchanged lasing intensity
The researchers quantified their material’s performance by measuring the amplified spontaneous emission (ASE) intensity of the two films as they were optically powered. They found that the ASE, or lasing, remained virtually unchanged after an hour at room temperature in air with a relative humidity of 55%. The lasing spectrum also maintained its narrowness (full width at half maximum) without shifting. The team stress that these measurements were taken without the films being encapsulated in glass, and without a protective layer over their tops, as was the case in previous ASE stability measurements of 3D perovskites such as MAPbBr3.
According to the researchers, the excellent stability of their material comes from the protection provided by the larger cations on its surface. “We have demonstrated the key role of triplets in the lasing process of these types of perovskites and the importance of managing triplets to achieve continuous lasing,” Adachi states in a Kyushu University press release. “These new findings will pave the way for the future development of a new class of electrically operated lasers based on perovskites that are low cost and easily fabricated.”
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