Thi Linh Hoang

Thi Linh Hoang

Snails climb up the well

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A snail climbs a well $x$ feet during the day, and during night, it slips $y$ feet. If the well is $h$ feet deep, how long will it take for the snail to climb?

Solution:

Let $k$ denotes the number of days for the snail climb up the well, $k \in \mathbb{N}$.

If $n \leq x$, $k = 1$.

If $n > x$,

  • If $ x \leq y$, $k = \infty$,
  • If $ x > y$ : k is the minimum value satisfies this inequality:
\[(k -1)(x-y) + x \geq h,\] \[\implies k - 1 \geq \frac{h - x}{x - y},\] \[\implies k \geq \frac{h - x}{x - y} + 1,\] \[\implies k = \lceil \frac{h - x}{x - y} + 1 \rceil\]

Review of Graph Transformer

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In last few years, Graph Transformers models become a promising direction for graph learning model due to the successful of Transformers in other tasks like NLP or CV. This note reviews about the recent works adapt Transformer for graph data for more a scaleable, expressive tool include improving positional encoding, attention mechanism, etc.

Note in Probability basis

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Some of the concepts of probability I think we will use frequently.