Hello World!

Welcome to my homepage! I've decided to create a page to publish personal projects and write-ups on.

What to expect

I plan to write about my personal research projects. This will include:

  • Exploring machine learning architectures
  • Implementation details of interesting models
  • Competitive programming content

Testing some features

As this is my first post, I'm testing different features:

Code snippet example

G = '2021$'
def get(x)
  dp = Array.new(20) { Array.new(5) { Array.new(2, 0) } }
  dp[x.size][4][0] = dp[x.size][4][1] = 1
  (x.size - 1).downto(0) do |i|
    (0..1).each do |under|
      (0..(under == 1 ? 9 : x[i].to_i)).each do |j|
        (0..4).each do |k|
          dp[i][k][under] += dp[i + 1][k + (G[k] == j.to_s ? 1 : 0)][under | (j < x[i].to_i ? 1 : 0)]
        end
      end
    end
  end
  dp[0][0][0]
end
k = gets.to_i
p (0..10**19).bsearch { |i| get(i.to_s) >= k }

Math rendering

Let G,KG, K be groups, and let ϕ:K→Aut(G)\phi: K \to \mathrm{Aut}(G). Further, let G′≅GG' \cong G with an isomorphism Φ:G′→G\Phi: G' \to G and K′≅KK' \cong K with an isomorphism Ψ:K′→K\Psi: K' \to K. Now,

G⋊ϕK≅G′⋊ϕ′KandG⋊ϕK≅G⋊(ϕ∘Ψ)K′, G \rtimes_\phi K \cong G' \rtimes_{\phi'} K \qquad \text{and} \qquad G \rtimes_\phi K \cong G \rtimes_{(\phi \circ \Psi)} K',

where ϕ′:K→Aut(G′)\phi': K \to \mathrm{Aut}(G') with ϕ′(k)(g′)=Φ−1(ϕ(k)(Φ(g′)))\phi'(k)(g')=\Phi^{-1}\left( \phi(k)(\Phi(g')) \right) for all k∈K,g′∈G′k \in K, g' \in G'.