HINF 6500 - Week 6

1

The project is intended to look at EEG power amplitude & breathing phase locking, and how this modulates attention.

• A = attention score
• B = function describe breath phase
• P = period in milliseconds
• t = time
• E = EEG gamma power amplitude

\[ lim_{coh \to 1^-} coh(t) = coh(B(t + P_{B}),E(t + P_{E})) = lim_{\beta \to 0^+} A \pm \beta\epsilon \\ \min_{\beta} \text{when} P_{B} = P_{E} \]

2

sir_table <- tabulizer::extract_tables("Martcheva - 2015 - Introduction to Epidemic Modeling.pdf", 
    pages = 9) %>% .[[1]]
nm <- sir_table[1, , drop = T][c(1, 4)] %>% as.character()
sir_table <- rbind(sir_table[-1, 1:2], sir_table[-1, 3:4]) %>% as.data.frame %>% 
    setNames(nm) %>% mutate_all(funs(as.numeric(as.character(.))))

\[I`( t ) = βI(N - I) −αI \\ \int_{}\]

a <- 0.476
b <- 0.002342
N <- 763
integrate(function(I, a, b, N) {
    b * I * (N - I) - a * I
}, lower = sir_table[1, 1], upper = sir_table[nrow(sir_table), 1], a, b, N)

## 120.4524 with absolute error < 0.0000000000013