• Peach:
  • response to cold stress
• Grape:
  • development related to seed and grape size (Sultaniye)
• Wine:
  • quality control on exported wine,
  • avoid secondary fermentation

• Salmon:
  • effect of diet on metabolism,
  • selection of stress tolerant families.
  • Whole genome sequencing
    • 10M dollars project,
    • harder than human genome
    • Chile, Canada and Norway
• Mining:
  • copper extraction helped by bacteria

We had a research contract with the main mining company

State owned, big enough to pay for long term research

We focused mainly on 2 questions:

• Monitoring the microbial community in the mine
• Understanding how these bacteria do “mining”

Microorganism live in the most diverse environments.
They are the key to:

• develop new biotechnology
• manage our natural resources
• improve our health
• understand our past

But only ~5% of them can be grown in the lab

If we know the DNA sequence for each relevant organism

• We can determine a “fingerprint” for each organism DNA
• That is, a short DNA sequence that is “unique” to each organism
• Length about 20 nucleotides
  • qPCR primers
  • microarray oligonucleotides

Ideally the primer probably binds to the organism DNA, and probably do not bind to others organisms.

N.Ehrenfeld, A. Aravena, A. Reyes-Jara, N. Barreto, R. Assar, A. Maass, P. Parada, Design and use of oligonucleotide microarrays for identification of Biomining microorganisms. Advanced Materials Research 71-73 (2009) 155-158.

• Method for the design of oligonucleotides for molecular biology techniques.
  • Australia, Mexico, South Africa, USA
• DNA fragments array from biomining microorganisms and method for detection of them.
  • Argentina, Australia, Mexico, Peru, South Africa, USA
• Array of nucleotidic sequences for the detection and identification of genes that codify proteins with activities relevant in biotechnology present in a microbiological sample, and method for using this array.
  • Australia, Chile, China, Mexico, Peru, South Africa, USA

• Method and array for detection and identification of microorganisms present in a sample by using genomic regions coding for different tRNA-synthetases.
  • Argentina, Australia, Chile, Mexico
• Method for the identification and quantification of microorganisms useful in biomining processes.
  • Australia, Chile, Mexico, South Africa, USA

Since most microbes cannot be isolated, and given current technology, the modern approach is:

• Sample all DNA from the environment
• Determine the sequence of each fragment
• Cluster similar sequences together

Of course the clusters depend on the distance we choose

Most of the sequences from environmental samples are unique

That is, they do not correspond to any known organism

The question is, given a DNA read, which are the “nearest” known organisms?

Here “closest” is in the phylogenetic sense

• Utilitarian
  • To pay the bills and not be cheated
  • To get the proper concentrations in the lab
• Practical
  • To design the experiments
  • To analyze the results of the experiment
• Philosophical
  • Understand the meaning of the results
  • Connect experiments with the rest of human knowledge

The limits of my language are the limits of my world

Ludwig Wittgenstein

Whereas throughout much of the 20th century computational and mathematical biology were niche disciplines, their methods are now becoming an integral part of the practice of biology across all fields.

Stefan et al. “The Quantitative Methods Boot Camp: Teaching Quantitative Thinking and Computing Skills to Graduate Students in the Life Sciences”. PLoS Comput. Biol. 11, 1–12 (2015).

It has been invented and developed independently in several places:

• ancient Babylon, ancient Egypt,
• ancient Greece (all around Mediterranean and Aegean sea),
• China, India,
• Pre-hispanic Mexico, Golden Age Persia,
• European Renaissance, Industrial England, Soviet Union, etc.

We have mathematicians in Turkish money.

• We need to learn math to receive this cultural legacy
• We speak about “Universal literature”
• Architecture
• Painting and Sculptures
• Music
• Cinema

Mathematic belongs to all humanity

It is something developed in our minds

It does not exist outside our brains

(although nature’s rules seem to be well described by math)

We need some training to appreciate its beauty

The same happens with art such as

• opera,
• cubist painting,
• modern ballet,
• abstract sculpture,
• and so on.

It is like moving in the city using only the metro:

easy, but you can only go to places that others have already prepared

These places are crowded, and it is hard to be noticed here.

It is like having your own car. Depending on your knowledge level, it can be

• a taxi (someone else drives),
• an sedan car (you drive on paved streets),
• a jeep (you can go to much more places, you can fix up when things break down), or
• an experimental autonomous car (you design a new car from the zero)

You need at least to understand enough mechanics to know

• when to put gasoline,
• When to change oil,
• maybe how to change a tire,
• How to talk to the mechanic so he does not cheat you.

• You do not need to calculate everything
• You do not need to solve everything
• You need to interact with other experts
  • Statisticians
  • Bioinformaticians
  • Computer Scientists
  • Applied Mathematicians

Many people has been told that math is about numbers

And computers can do that faster and easier

Do we still need to learn math?

Yes, because computers do not solve problems

Mathematics solves problems. Then computers solve them fast

To have correct answers we must ask the correct questions

This is the real reason we need math

Mathematics is not about numbers, equations, computations or algorithms: it’s about understanding

William Paul Thurston (1946 – 2012),
American mathematician

• Most people say math is “doing things with numbers”. In other words, when we say mathematics, people thinks of arithmetics
• Geometry is even older. More than 6000 years old
• we also learned set theory in primary school

In my opinion, scientists need three fundamental tools

• Logic
• Probabilities
• Single variable calculus

Biologists need also two practical tools

• Matrices
• Networks

This has been discussed a lot

There are several combined reasons

Let’s see some of them

1. Survival
2. Save energy

So System 1 is the default mode

Most of the time we use the cheap intuitive system

Rational thinking (i.e. math) is not spontaneous

• Sometimes the purpose is not clear
• It is hard to learn something if we don’t know why we are learning it
• Unfortunately, in many cases we cannot understand the purpose until we learn a little

These people are “pure mathematicians”

In real life, many mathematical theories have been developed as “games” that mathematicians play, something amusing or beautiful.

Therefore people invented the math before having a real-world motivation.

For example: non-Euclidean geometry is essential to Einstein’s General Relativity, but was invented 50 years before, as a game

As we said, mathematics is a superpower

Some people already has that power

And they do not want to share it

• Through history, high impact mathematics has been know only by few people
• only few people knew the really important mathematics
• In most societies, mathematics has high social value, because it is difficult and exclusive
• Today, elite mathematics gives “special authority” to people who is already powerful

Scientific American, August 2016

• Today big companies have immense power because they have models of people’s behavior
• They even pay you 2% to get your Big Data
  • Supermarkets give fidelity cards with discounts
  • Airlines give free flight if you register
• “Knowledge is Power”

One of the powerful (and difficult) aspects of math is abstraction

1. dealing with ideas rather than events: topics will vary in degrees of abstraction.
2. freedom from representational qualities in art: geometric abstraction has been a mainstay in her work.
3. the process of considering something independently of its associations, attributes, or concrete accompaniments: duty is no longer determined in abstraction from the consequences.

• it is easier to solve a problem when we discard irrelevant details
• Abstract problems can correspond to several applied problems
• Solving one solves all of them
• These connections help us to understand new problems by analogy to old ones

If two different problems are connected, we can change perspectives from one to the other

For example, analytic geometry connects algebra and classic geometry

We will do this a lot

The following is s problem from Diophantus’s Arithmetica.

Given two numbers, to add to the lesser and to subtract from the greater the same (required) number so as to make the sum in the first case have to the difference in the second case a given ratio.

Given a and b and a ratio ρ, find x such that a + x = ρ(b − x).

• Good mathematical notation should make it easier to understand the problem, and to find the solution
• Mathematical notation is (almost) universal. It helps to communicate ideas
• Careful notation keeps us honest. It is harder to fool ourselves when we write explicit formulas.

This course: “Tools for thinking”

• Logic
• Probabilities

The other course: “Tools for modeling”

• Matrices
• Vectors
• Linear models

• “How to solve it” G. Polyá
• “The Language of Mathematics: Making the Invisible Visible” Keith Devlin
• “Introduction to Mathematical Thinking” Keith Devlin
• “Maths from Scratch for Biologists” Alan J. Cann
• “Understanding Comics: The Invisible Art” Scott McCloud