remove seeds from images and increase contrast between normal and abnormal brain tissues
Speaker:
power barrier ( battery capacity size)
OLED
GPS:
GPU
DNN
typical type of Gamma, $\alpha = r/2, \theta = 2 = 1/\lambda$
where r is called the degree of freedom
eg: Brown motion: $x = Normal,y = Normal, then, r = \sqrt{x^2 + y^2} = \sqrt{chi-square}$
$\alpha$ = power (decay) law
how to solve: modular code?
一位local女教授，既Jimmy之后第二位不准手机铃声的教授。。。
第一节课是拿一个英文的科普视频 放一段讲一段。。。太真实了吧？。。。
A cycle is a path with at least three edges, in which the first and last nodes are the same, but otherwise all nodes are distinct.
the edge joining two nodes if deleting that edge would cause the two nodes in two different components.
Bridge is rare
the edge joining nodes A and B, if its endpoints A and B have no friends in common.
the distance between the end points if that edge were deleted.(original:1)
Embeddedness of an edge in a network is the number of common neighbors the two endpoints have.
Embeddedness(Local bridge) =0
A graph is connected if for every pair of nodes, there is a path between them
For each pair of nodes A and B: 1 unit of traffic “flow” from A to B if A and B belong to same component. the flow divides itself evenly along all the possible shortest paths from A to B
朋友的朋友更容易成为朋友
a的朋友们也互相是朋友的概率
如果a 和bc关系很好，那么bc会成为朋友。
如果不是(no matter strong or weak)，violate the property
no of nodes who are neighbors of both A and B**/** no of nodes who are neighbors of at least one of A of B.
Weak ties provide the more crucial(关键) connective structure
• for holding together disparate communities and
• for keeping the global structure of the giant components intact.
移除最可能连接两大块的（betweenness最大值）
把nodes that are likely to belong to the same region merge起来
The tendency of individuals to associate and bond with similar others
Homophily Test: If the fraction of cross-gender edges is significantly less than 2pq(p = fraction of males,q = fraction of females), then there is evidence for homophily.
The edge is heterogeneous(异质) if two end nodes do not share the same characteristic
select friends with similar characteristic. tends to drive the network towards smaller clusters of like-minded individuals (balkanization)
modify their behaviors to bring them more closely into alignment with the behaviors of their friends.
– reverse of selection
– Involves mutable characteristics
– 近朱者赤， 近墨者黑/lies down with dogs, rises with fleas
can produce network-wide uniformity, as new behavior spreads across the links.
Include the contextual factors (the set of activities) into the network. expressed as a bipartite(even)
graph.
• A graph is bipartite if its nodes can be divided into two sets in such a way that every edge connects a node in one set to a node in the other set
• Two people sharing the same focus → an opportunity to become friends.
Extension:
How global patterns of spatial segregation can arise from the effect of homophily operating at a local level (Thomas Schelling)
homophily draws people together along immutable characteristics
The Schelling model creates a natural tendency for mutable characteristics
clique/complete graph: graph which an edge connecting each pair of nodes
A complete graph is structurally balanced if its everyone triangle is balanced.
If a labeled complete graph is balanced, then
There is no set of three nodes such that the edges among them consist of exactly two positive edges and one negative edge . ( all are enermy are possible)
A signed graph is balanced if and only if it contains no cycle with an odd number of negative edges.
If at least 99.9% (1-$\epsilon$)of all triangles in a labeled complete graph are balanced, then
– Informational effect :
Network effect (direct benefit effect) :(C5)
you incur an explicit benefit when you align behavior with the behavior of others.
$P(A|B) = \frac{A\cap B}{B}=\frac{P(A)P(B|A)}{P(B)}$, 一般 ，pa, p(b|a)题目都给了。问题是求pb：
若A好算:$p(b) = P(A)P(B|A)+P(A^c)P(B|A^C)$
States: G(Good) with probability p, and B with 1-p
Accepting select which state
Private information
Signal H(High) before making decision: accepting is a good idea, L(Low) : bad idea
P(H|G) = q > 0.5, P(L|G) = 1-q < 0.5
Payoff: 0 reject. Vg: accepting a good option Vb: accept a bad option
Suppose one receives a H signal
S = a high signals + b low signals
situation that the welfare of an individual is affected by the actions of other individuals
the max amount one is willing to pay for one unit of the good. If consumer x (0 ≤ x ≤ 1) has a higher reservation price r(x) than consumer y, then x < y.
**r: strictly decreasing **
p’: production cost of one unit of the good (the minimum price a producer is willing to accept to sell a good)
x’: equilibrium quantity of the good so that r(x’) = p’
intrinsic interest. r(x). eg. r(1 ) = 0
the no. of other people using the good
reservation price of consumer x = r(x)f(z) . here z is the fraction expected by x
self-fulfilling expectations equilibrium p’ = r(z)f(z)
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z^: fraction of population who buy the product (actual buyer)
r(z^)f(z) = p = >
z^ = $r^{-1}(p/f(z))$ = g(z)
For goods with network effects, the equilibria are typically not social optimal.(社会所有人的总利益)
Being the first to reach this tipping point is more important than being “best”.
f(Z) = 1 + az^2
r(X) = 1-x
Central Limit Theorem says that if we take any sequence of small independent random quantities, then in the limit their sum (or average) will be distributed according to the normal distribution.
A function that decreases as k to some fixed power, such as 1/k 2(fraction) is called a power law
Model the growth of the popularity.
preferential attachment: : “preferentially” to pages that already have high popularity. (人们更愿意打开已经火了的页面,copy别人的)
No. of in-links of node j = $x_j = p/q[(t/j)^q-1]$ . t: simulated steps. q = 1-p
At time t, we have nodes x1, x2, … xt. The fraction of nodes with at least k links is
$[\frac{q}{p}k +1]^{-1/q}$
f(k) = the fraction of nodes with exactly k links = $1/p [1+\frac{1-p}{p}k]^{-(1+\frac{1}{1-p})}$. when p -0, power law exponent is 2.
a small set of items that are enormously popular
Zipf’s Law : the frequency of the j th most common word in English (or most other widespread human languages) is proportional to 1/j.
Structure of the network and how individuals are influenced by their particular network neighbors (instead of everyone else in C5)
the set of initial adopters causes a complete cascade at threshold q(大于百分之多少才换）.
cluster of density p = a set of nodes such that each node in the set has at least a p fraction of its network neighbors in the set.
cluster of density 1:
Heterogeneous Thresholds： each node has a specific payoff and hence threshold
A blocking cluster in the network is a set of nodes for which each node v has more than a 1 − qv fraction of its friends also in the set.
cascade capacity of the network: 有限初始集能造成complete cascade的最大threshold
最大值：1/2
proof number of AB edges is decreasing when switching w from B to A
payoff from choosing A = a’（两边都是A/AB) 则double a
payoff from choosing B = b’
payoff from choosing AB= a’+b’-c
Two type of links:
Homophily(和其他r个小格内点相连的link)and
Weak ties(剩余的k 个远link).
time: at most a2(log n)^2
The probability that a random edge from center point v links into any node in this group is approximately independent of the value of d. ( in d - 2d circles)
rank(w) = the number of other nodes that are closer to v than w is. (比w 还离v近一点的)
dist(v, w) = the social distance between nodes v and w = the size of the smallest focus that contains both v and w
A link between each pair of nodes v and w with probability proportional to dist(v,w)^-p
Efficient decentralized search when p = 1. 17
•The basic reproductive number ( R0) = the expected number of new cases of the disease caused by a single individual = p(probability)k(new meet num).
Percolation : static view of the model. edge v-w is open is w is infected by v
SIR . susceptible infectious removed
SIS susceptible infectious back_TO_susceptile
SIRS susceptible infectious 免疫期 back_TO_susceptile
transient contacts — contact networks in which each edge is annotated with the period of time during which it existed
qn = the probability that the epidemic survives for at least n waves
q∗ = qn when n is infinite = the probability that the epidemic persists indefinitely.
consider the time that k个个体是一个祖先
1960s: Search repositories of newspaper articles, scientific papers, patents, legal abstracts, and other document collections in response to keyword queries.
vote by link 缺点：offtopic, criticism, advertisement
each page有两种score
authorities 权威网站 更新： 所有指向他的page的hub score和
hub 首页 更新 类似
1 | initial are score = 1 |
(A-\lamda I)x = 0
\lamda = eigenvalue
x = eigenvector
每个node指出k个，其value平均分k，到新的node。
最后把收到的value sum。
sum之后乘以一个factor 。 然后把factor多出来的那一部分均匀分给每个人。
随便选一个。然后继续选out-going的。和pagerank思路一样。停在哪个page的概率和pagerank概率一样。
SPONSORED SEARCH AD:关键词
branding ad ：直接投放在网站上
contextual ad： 根据用户特征投放广告
click-through rates：（r_i) The number of clicks per hour it will receive
revenue(收入) v_j per click of advertiser j,
ri*vj = benifit
if the search engine knew all the advertisers’ valuations for clicks
For buyer:
$v_{ij}$ = valuation for item i by buyer j
$p_i$ = price announced by the seller
v- p 就是买家收益。
Market clearing prices 所有买家选到最赚的而且不冲突
price先重置为0
将最多人要买的slot price 加一
重新计算
重新加一
直到可以market clearing
the advertisers’ valuations are not known
算没有 A 后 BC 收益。比如600
有A后BC收益 比如 200
那么A 需要支付 600-200
bi bids per click
GSP charges a cumulative price of ri bi+1 for slot i.
The pair of strategies (S; T) is a Nash equilibrium if S is a best response to T, and T is a best response to S.
Best response: $P_1(S,T)>= P_1(S’,T)$ T: stratage of 2
STrict: 没有等于。
Dominant strategy： a strategy that is a best response to every strategy of Player 2.
A strictly dominant strategy .
这一年来眼睛经常感到疲倦，再加之镜腿断了，于是想要换个合适的眼镜。
换眼镜也是换出了很多学问，索性记录一下。
第一件事是决定怎么买，参考网上各论坛建议，选了三种方案。
淘宝镜片 + 淘宝镜架 + 香港验光
深圳眼镜
香港眼镜
因为镜腿断了，急着要用眼镜。而另外两个都有明显缺陷（淘宝太久，深圳太远而且怕被宰）
决定在香港买眼镜后发现事情没那么简单。香港眼镜店对我来说也分了三种选择。
还能怎么办，一个一个比较，看呗。
另外在香港论坛查了许多，又恰逢发现小米有镜架（249），蓝光眼镜（99）卖。查了下都是钨钢材质，虽然听不懂但对小米的品质还是有信心的，于是买了个蓝光眼镜拆了镜片做镜框。（客服说99的镜框和249的镜架材质重量设计都一模一样= =，唯一区别是一个韩国，一个国产。。。）
镜架有了，一个一个去问镜片。
香港好的一点是，说我再去其他地方看看不会尴尬，店员都很爽快。
总共问了6个店子。
熟人推荐，瑞士宝1.61非球面300+防蓝光200 = 500。在那才知道。。我戴了三年的眼镜。。。戴！反！了！
难！怪！一！直！头！晕！
难！怪！一！直！掉！镜！片！
只有一个说广东话的老头，这种看起来挺靠谱的。
阿波罗1.61非球面290+防蓝光200 = 490
装修的和内地有点像，但是听到 依视路880？不确定听没听错。
DULUX1.61蓝光 = 700
依视路1.61蓝光 = 1300
豪雅？不确定是否为EGG特供。
1.61非球面600 + 蓝光100 = 700
1.67非球面900 + 蓝光0 = 900
一家日本的连锁平价眼镜，在香港很受欢迎。
因为暂时只在太古城有店，所以电话问了下。
最终看了下，大概就是一般品牌500，豪雅700值得考虑。又想了下豪雅这么便宜！还要什么飞机！淘宝上买镜片都不止这个价了。最终手机没电了，不想再来所以入手EGG豪雅。。
值得一提的是香港的验光确实多了些没体验过的环节，总的来说感觉上专业一点。
遗憾:
最后买的有点仓库，没考虑几点:
不过总的来说觉得700验光+豪雅已经是很不错的了，具体是什么豪雅 后天就知道了（特意叮嘱了给我留着镜片包装）
眼镜到手，试戴半天后效果特别好，真的看电脑久了不头晕了！不过也可能是之前一直是反的原因。
镜片包装也如约给我了：
包装上没有任何豪雅的资料，电话问了豪雅的人确定确实egg有用，找工作人员，工作人员加了我微信，说可以给我一个我自己镜片的豪雅证明，里面也会specify具体是哪一款豪雅镜片。
总之是一次特别棒的体验
本着所有东西都要体验一下的高尚理想，这次(2019.10)配眼镜选了另外一种方法…网上听热门的 日本JINS网店 海淘。
因为自己海淘的挺多，加之性价比确实蛮高的，500+可以有一个1.74折射率的HOYA眼镜，还是钛金属的镜框（镜架是塑料。。）也是挺满意的说。
另外打算下次配眼镜要么去日本线下？顺便还可以去玩下。要么就去知乎的深圳眼镜热店。
生活就是折腾才有意思啊哈哈~
CUHK CSCI5030
instructor: XU Lei
来自 交大 的大佬教授。
大佬就是大佬，直接用中文。
四年来第一次上中问的专业课，感觉exciting。
$P(d) = log_{10}(d+1)-log_{10}(d)$, where d is the case that the first digit of the data is d
Sample space: $S$
event:
$P(A|B) = \frac{P(A\cap B)}{P(B)}$
$P(A) = \sum{P(A\cap B_i)}$
Now: We want to know: if A happened, what are the p of different B?
$P(B_j|A) = \frac{P(A\cap B_j)}{P(A)}$
$P(A\cap B_j) = P(A|B_j)P(B_j)$
Consider a partition $B_j$ of $S$ and event $A$:
$P(B_j|A) = \frac{P(A\cap B_j)}{P(A)}= \frac{P(A|B_j)P(B_j)}{\sum{P(A|B_i)P(B_i)}}$
$B_j = C_2|X_1, A = H_3|X_1$
Mean is the quantity a that minimizes $min_aE(X-a)^2$
Variance $(x-E(x))^2$
Moment generating function = mgf = summary of the overall random behavior
median $min_b |x-b|$