Processing math: 100%

Logarithmic scales

Computing for Molecular Biology 1

Andrés Aravena, PhD - Istanbul University

December 10, 2019

How cells grow

Cells in a culture grow every day

We want to know the number of cells every day: ncell[t]

Here t is the time in days.

We start with an initial number of cells, that we call initial

Each day, the number of cells increases by a factor rate

$\texttt{ncell[t]} = \texttt{initial} \cdot \texttt{rate}^\texttt{t}$

Graphically

plot(t, ncell)

We cannot see what happens when values are small

Logarithmic scale (“semi-log”)

plot(ncell ~ t, log="y")

We can see better using a logarithmic vertical scale

Size of the culture

When the cells grow in a petri dish, then the culture will form a circle

The area of the circle is proportional to the number of cells.

Thus, the circle radius changes with time following this equation $\texttt{ncell[t]}=K \texttt{r}^2$ in other words $\texttt{r}=\sqrt{\frac{\texttt{ncell[t]}}{K}}$

Log-log scale

par(mfrow=c(1,2))
plot(radius ~ ncell)
plot(radius ~ ncell, log="xy")

Kleiber’s Law

(Physiological Reviews 1947 27:4, 511-541)

Relation of Body size v/s metabolic rate

Same in log-log scale

We saw the same in Homework 5

plot(income~population, world)

Using log-log scale

plot(income~population, world, log="xy")

Same, with colors and point size

plot(income~population, world, log="xy", pch=16,
     col=region, cex = 3*sqrt(area/max(area))+0.1)

Exponential growth in Science and Technology

Moore’s Law

A idea from ~1970, by George Moore (Intel)

The simple version of this law states that processor speeds will double every two years

More specifically, “the number of transistors on a CPU would double every two years”

(see paper)

Intel says

Real data: Number of transistors in chips v/s year

plot(count~Date, data=trans)

Semilog scale: Number of transistors v/s year

plot(count ~ Date, data=trans, log="y")

Same happens with DNA

Cost of sequencing human genome

Months since Sept 2000

What does this mean for you?

The Robots Are Coming

John Lanchester

1992 Russo-American moratorium on nuclear testing
1996 Computer simulations to design new weapons
Needed more computing power than could be delivered by any existing machine

The Robots Are Coming

John Lanchester

USA designed ASCI Red, the first supercomputer doing over one teraflop
- ‘flop’ is a floating point operation (multiplication) per second
- teraflop is $10^{12}$ flops
In 1997, ASCI Red did 1.8 teraflops
The most powerful supercomputer in the world until about the end of 2000.

The Robots Are Coming

In his book, John Lanchester says

"I was playing on Red only yesterday – I wasn’t really, but I did have a go on a machine that can process 1.8 teraflops.

"This Red equivalent is called the PS3: it was launched by Sony in 2005 and went on sale in 2006.

The Robots Are Coming

"Red was [the size of] a tennis court, used as much electricity as 800 houses, and cost US$55 million. The PS3 fits under the TV, runs off a normal power socket, and you can buy one for £200.

"[In 10 years], a computer able to process 1.8 teraflops went from being something that could only be made by the world’s richest government […], to something a teenager could expect [as a gift].