2019/2/18
Problem1 A G(V, E), with each edge is capacity $C_e$.
The is source s $\in$ and sink t $\in$ V.
No edge enter and and no edge leaving t.
Flow is defined as function f that take the edge and return a nonnegative real number, $f: E \rightarrow R^+$
Subjects to following constraints
$0 \leq f(e) \leq c_e$ $\sum_{e\ into\ v} f(e) = \sum_{e\ out\ of v} f(e)$ or $f^{out}(v) = f^{in}(v)$ GOAL: find the maximum flow.……
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2019/2/14
Constrained Optimization $$\min_{x \in R^n} f(x)$$
subject to: $$c_i (x) = 0, i \in E \text{(equality constraints)}$$ $$c_i (x) \geq 0, i \in I \text{(inequality constraints)}$$
Feasible Set $\Omega = { x_i | c_i(x) = 0, i \in E \text{ and } c_i(x) \geq 0, i \in I}$.
Case 1 $\min_{x \in R^n} f(x)$ subject to $c_1 (x) = 0$
x is local minimum if x + s $\notin \Omega$ or f(x+s) $\geq$ f(x).……
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2019/2/12
Full Stack Developer
Front-End Basic
HTML5 CSS JavaScript Framework
Angular React Vue Back-End Ruby on Rail Python with Django Java Database MySQL MongoDB Tools Docker AWS Knowledge Front End CSS preprocessors Sass or LESS……
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2019/2/9
Problem1 Sequence Alignment
We can reduce the space by using only two column instead.
Space-Efficient-Alignment(X ,Y)
Array B[0…m,0…1] Initialize B[i,0]=iδ for each i (just as in column 0 of A) For j=1,…,n B[0,1]=j$\delta$ (since this corresponds to entry A[0,j]) For i=1,…,m B[i, 1]= min[$\alpha x_iy_j$ + B[i − 1, 0], $\delta$ + B[i−1,1], $\delta$ + B[i,0]] Endfor Move column 1 of B to column 0 to make room for next iteration: Update B[i, 0]= B[i, 1] for each i Endfor However, this doesn’t left enough information to get back the information about alignment.……
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2019/2/9
Problem1 When you type “ocurrance”, the brower will will prompt “Perhaps you mean occurrence?”
How does the search engine knows?
How does it know the most similar word?
How do we determine the similarity between words?
The definition of similarity will be based on the optimal alignment between X and Y where X = $x_1x_2 … x_m$, Y = $y_1y_2 … y_n$.
when there is gap (character not matched), we pay $\delta$ when we match character p and q, we pay $\alpha_{pq}$, where $\alpha_{pq}$ = 0 goal is to minimize the sum of cost.……
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2019/2/9
Problem1 We have bases of {A,C,G,T} in DNA sequence, where A-T and C-G form a pair. A sinlge strand of RNA will loop back, resulting shape called secondary structure.
Let $B = b_1b_2 … b_n$, where $b_i$ = {A,C,G,U} also A-U, C-G form pair
Then the Secondary structure, S ={(i, j)}
no sharp turn, i < j - 4 pair is either {A,U}, {C,G} (either order) no base appear in more than 1 matching no crossing condition, (i,j) and (k, l) $\in$ S, we can’t have i < k < j < l Algorithm Following the same analysis……
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