The second phase of the Barnaby & 7th affordable housing redevelopment project in Washington Highlands, D.C. has been officially closed by Gilbane Development Company, MED Developers, Equity Plus Manager LLC, and Housing Help Plus. This partnership marks a significant milestone in the creation of a more inclusive and supportive community within the neighborhood.
This phase will consist of four distinct buildings along Barnaby Street with a total of 229 units. Yarojin Robinson, Senior Vice President at Gilbane Development Company for Mixed-Income and Affordable Housing expressed excitement about this progress towards their goal.
The overall project is divided into three phases which will result in 470 new units while also preserving existing tenants. The first phase is currently under construction and expected to be completed by early 2025 with a mix of one-, two- ,and three-bedroom units. Construction for Phase II is set to begin in February 2025.
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In order to calculate $P(A|B)$ we use Bayes’ theorem:
$$P(A|B) = \frac{P(B|A) P(A)} {P(B)}$$
where $A$ represents our hypothesis or event that we are interested in (e.g., “the patient has cancer”)
and $B$ represents evidence or data that we have observed (e.g., “the patient tested positive for cancer”).
To understand how this formula works let’s break it down into its components:
1) Prior probability: $P(A)$ \\
This term represents our initial belief about the likelihood of event A occurring before taking any evidence into account.
For example if there was no information available about whether or not someone had cancer,
we might assume that they have a 1\% chance of having cancer ($P(A) = 0.01$).
2) Likelihood: $P(B|A)$ \\
This term represents the probability of observing evidence B given that our hypothesis A is true.
For example, if we know that someone has cancer (hypothesis A),
the likelihood of them testing positive for cancer (evidence B) might be high ($P(B|A)=0.95$).
On the other hand, if we know that someone does not have cancer,
the likelihood of them testing positive for it would be low ($P(B|A)=0.05$).
3) Evidence or marginal likelihood: $P(B)$ \\
This term represents the overall probability of observing evidence B regardless
of whether our hypothesis is true or not.
It can also be thought as a normalization factor to ensure that all probabilities add up to one.
Putting these components together in Bayes’ theorem allows us to update our initial belief about event A based on new evidence B.
In other words, it helps us calculate how likely event A is given what we observed in event B.
To illustrate this concept with an example,
let’s say there’s a rare disease called “X” and only 1 out every 10000 people have it ($ P(A)= \frac{1}{10000} = 0.0001 $).
We want to test for this disease using a diagnostic test which has been shown
to correctly identify X-positive individuals with accuracy rate at $\frac{99}{100}$($ P(Positive | X )= \frac{99}{100} = .099 $.)
Now let’s imagine you took the test and got back results saying you tested positive!
What are your chances now? Are they higher than before?
Let’s use Bayes’ theorem:
$$ P(X | Positive )= \dfrac {(\dfrac{99}{100}) \times (\dfrac{1}{10000})} {P(Positive)} $$
We know that $ P(Positive) = (P(X) * P( Positive | X )) + (P(X^c ) * P( Positive | X^c )) $
$= (\dfrac{1}{10000} *\dfrac {99}{100}) + ((\dfrac{9999 } { 10,000 }) *\dfrac { 1 } {(10,000 – 9999)})$
$= .0098$
Therefore,
$$
\begin{aligned}
P(X|Positive)&=\displaystyle\dfrac{\left(\displaystyle\dfrac{(0.99)(0.0001)}{(0.0098)}\right)}
{\left(\displaystyle\dfrac{(0.01)(-9987/9999)+(9987/9999)*(2/3))+(9975/9996)*(4*9975+19995)/20000}\right)}
\\&=.002
\end{aligned}
$$
So after getting a positive test result,
our chances of having the disease have increased from $\sim$ .001 to $\sim$.002.
This may not seem like a big difference but it is actually twice as likely now!
This shows how Bayes’ theorem can help us update our beliefs based on new evidence and make more informed decisions.
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% _SHANG_
The Shang dynasty or Yin dynasty (/��������/[2]) was the second dynasty in Chinese history,[3] lasting from c.\��1600 – c.\��1046 BC.[4][5] According to the traditional chronology based upon calculations made approximately 2,000 years ago by Liu Xin,[6] the Shang ruled from 1766 BC to 1122 BC, but according to the chronology based upon the “current text” of Bamboo Annals,[7][8][9] they ruled from 1556 BC to 1046 BC. The dynasty was founded by Tang of Shang.[10]
The capital city was Yin (��), also known as Yin and Zheng in Chinese historiography. It is believed that it was located in present-day Anyang, Henan Province, on a bend of the Yellow River.
The Xia–Shang–Zhou Chronology Project concluded that there could be no material basis for either early date.[11]
The dynasty’s many capitals were likely located in several locations throughout northern China including Chaoge (in modern Linfen City), Ao (modern Luoyang) and perhaps even Xi’an[citation needed], which had been Qin’s capital city during later periods.
Yinxu
Yinxu (/��j��n����u��/; Chinese: �����; literally: ‘Ruins of Yin’) is an archaeological site located near Anyang City, Henan Province, China. It is one of China’s oldest and largest archeological sites with an area over three square kilometers containing ruins dating back almost four thousand years.
Historical background
In ancient times Yinxu served as a capital city for numerous dynasties such as Western Zhou Dynasty[12]. Later on it became famous through oracle bones inscriptions used for divination practice during late Shāng period [13].
Archaeological history
Excavation work at Yinxu began under archaeologist Li Ji who led excavation efforts between year1961-1963[14]. After his death he was succeeded by Xia Nai who continued the excavation efforts till 1978[15]. During this period, numerous artifacts were discovered including oracle bones inscriptions which provided valuable information about Shāng dynasty [16].
In 1983, Yinxu was declared as a UNESCO World Heritage Site. Since then it has been protected under Chinese law.
The site
Yinxu is located on the bank of Huan River near its confluence with Luo River. It covers an area of around three square kilometers and contains remains dating back to late Neolithic period (ca. 4th millennium BC)[17]. The most important discovery at Yinxu are oracle bones inscriptions used for divination practice during late Shāng dynasty[18].
Archaeological discoveries
The ruins at Yin have been excavated over many years but only a portion of it has been excavated.[19] The entire city is about two and half times the size of Beijing’s Forbidden City[citation needed], or ten times that[citation needed]of London’s Buckingham Palace.
Oracle bone script
Oracle bone script refers to incised ancient Chinese characters found on oracle bones which were animal scapulae or turtle plastrons used in pyromantic divination in ancient China.[20][21]
Early history
Shang Dynasty Oracle Bone Script from Anyang
Chinese bronze inscriptions
Bronze edict plate with Tangut characters
In terms chronology, there are several different versions regarding when exactly “the first” Zhou state conquered “the last” Shang ruler; some modern scholars propose dates such as c.\��1046 BC,[22][23] c.\��1042 BC,[24][25] or even c.\��1027–c.\��1012 BC.[26]
According to texts such as Records of the Grand Historian (compiled by Sima Qian), Yu the Great or Yu’s son Qi of Xia were said to have defeated a bronze-headed, six-armed monster called Kui (��) who had gorged himself on the children of people before he was killed by either Huangdi, Zhuanxu or Shaohao.[27] This monster is often associated with Chi You who also appears in later myths as one of “the Three Sovereigns and Five Emperors”.
The Records recount events from the reigns of Tang Shang Yi Yin (c.\��1600 BC – c.\��1580 BC), Tai Jia,[28] Tai Wu,[29][30][31] Pan Geng[32], Xiao Xin[33], Bu Bing [34](c. 1354–1322 BCE)[35]
According to Sima Qian’s chronology, King Wu Ding ordered his people to build defensive walls; this event is dated around 1300 BCE by McNaughton & Dreyer.
King Zhou
King Zhou was known for his extreme debauchery which led him into neglecting matters state. His behavior caused widespread anger among many nobles and officials which eventually resulted in an open rebellion led by Jiang Ziya.[36]
Jiang Ziya advised that Ji Fa overthrow King Zhou and establish a new dynasty but Ji Fa refused fearing backlash from other vassal lords. However after several years when he finally agreed Jiang Ziya instructed him how to defeat king zhou using guerilla tactics instead direct confrontation.
In year 1046 B.C., forces loyal to Western Zhou overthrew Shāng dynasty resulting end their rule over China.
Legacy
Shāng Dynasty left behind numerous cultural legacies including oracle bones inscriptions used divination practice during late period[citation needed]. They are considered oldest surviving form Chinese writing system[citation needed].
Another legacy left behind them includes development of bronze metallurgy which later on became integral part Chinese culture[citation needed].
The Shāng dynasty is also credited with the invention of a calendar system based on astronomical observations. The calendar was used to determine auspicious days for important events such as hunting, planting and harvesting.
Shang society
Social structure
During the Shang dynasty, China was ruled by a monarchy headed by a king (��) who served as both religious and secular leader.[37] Beneath him were several layers of nobles including dukes (公), marquis (��), counts or earls (��) and viscounts or barons(子).[38]
Below them were commoners including farmers, artisans merchants etc. At bottom social hierarchy stood slaves who worked in palaces temples etc[39].
Religion
In ancient times religion played an important role in everyday life during shāng period [40]. They believed that their ancestors had influence over their lives hence they
