# Difference between revisions of "CSSS 2008 Santa Fe-Tutorials"

### From Santa Fe Institute Events Wiki

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Brothers Foster rulez! I'll be there. [[Petr Svarc|Petr]] | Brothers Foster rulez! I'll be there. [[Petr Svarc|Petr]] | ||

Count me in! [[User:Giovanni|Giovanni]] | |||

==Linguistics== | ==Linguistics== |

## Revision as of 07:39, 9 June 2008

## The big opensource tutorial

### Open Source research software

Update! Tutorial scheduled on Monday 9 from 7:00p

Open (no pun intended...) your eyes to the wonderful world of FOSS -- Free and Open Source Software. While the distinction between Free and Open Source is a very interesting one (and highly contentious in the right crowds), for research purposes, we want to use the best tools for the job but some of us suffer from limited income, so I would like to talk about both. At the same time, FOSS is great to use for a non-economic reason: if you find bugs, or design extensions, you can fix them yourself (in OSS, at least) or at least report the problem back to a typically active community. Some potential tools to discuss/explore: R, Octave, Scilab, Gnuplot, perhaps some of the more useful languages in the field like Python and perhaps others I don't know as much about (a quick `apt-cache` on my Ubuntu Hardy install shows RasMol, ClustalW, SeaView, Achilles, complearn, EMBOSS, GENESIS, etc...)

- I would like to give a "Brazilian" contribution. Those who are interested in GIS&Cia could have a look at Free and Open Source GIS Source. Flavia

I would be happy to contribute a little bit about freely available simulation environments like ns-2 (computer networks) and omnet++ (a generic DES) -- Laura

- For Python I can offer a tutorial (see below). Nish, do you have any experience with Sage? Giovanni

All great ideas and I would love to have more of a "You know how to use this tool or you know of this tool, you talk about it" style of tutorial :) Maybe we can do a general OSS tutorial/discussion and then transition to specific sub-topics in separate tutorials (Python, GIS, networks, etc)? I've not used Sage, before, but I'm happy to take a look before the tutorial. Thanks for the info, Giovanni!

I'd like to learn more about open software. Paul

Some subtopics that we'll cover:

#### R tutorial

I (*Ruben*) know a little bit about R (basic stuff such as common plots and regression analysis) but would like to enhance my R skills. Does anybody have an interest in a R tutorial, too? Please edit this if there is more interest.

I am fairly familiar with R and could probably run a tutorial... what are you all interested in learning? - Skyler

- I'd just like to get an understanding of some of it's practical uses. -Devin
- Do you familiar with running social network analysis package in R? I want to learn more about it. Jiang

Interested folks

#### Python tutorial

I've (*also Ruben*) interest in a Python tutorial. Please edit this if there is more interest.

I can give a tutorial on python and on scipy/numpy. I can also talk about coding in general, as python is both a languange which is object oriented, imperative and functional (somehow). We can use the python tutorial itself as a reference for the part about the language, and then move to the basic concepts of the duo numpy / scipy, which form a powerful tool to manipulate n-dimensional arrays of numbers and also talk about ipython (the enhanced interactive shell) and the pylab interface, which gives a very nice environment for interactive programming and data analysis. Since pylab has been designed to mimic MATLAB's interface (the major plotting/statistical functions work as expected in both enviroments, which saves you a lot of time if you're used to MATLAB), I can also talk a bit about MATLAB, but being not a big fan of it, it would be better if somebody else stepped in to another tutorial on that.

Leave a mark if interested! Giovanni

I'd be interested in this as well Mark

I'm in. —Josh

I'm in. Nish

Yes please. Molly

Me too. Rory_Sayres Sayres 23:55, 4 June 2008 (MDT)

I'd be interested in this as well Tanja

I'm in Riley_Crane

Another one. Petr

## Neutral models in biology

Already met. Big thanks to Molly!

There is an interesting paper by Cosma Shalizi of SFI about methodological problems in social sciences research in which he talks about the concept of neutral models in evolution models. I was wondering if any of the bio-people can give a tutorial on this topic as I am pretty interested in understanding the concept. Giovanni

I would be very interested in learning about neutral networks too! - Skyler

## GIS / Spatial Analysis

Space Matters!! Geographical information system (GIS) is a computational system (hardware + database engine) that is designed to assemble, store, update, analyze, manipulate, and display geographically referenced information (data identified by their locations).

I'm thinking about introducing some basic GIS concepts and a free GIS software known as Terraview. We could also explore some spatial analysis techniques (this is the best part!) using Terraview and GeoDa (also free!).

Please edit here if you are interested or send me an email. Flávia

Update! It has been scheduled on Friday, June 13 from 1:30 p.m. - 2:45 p.m.

I'm in Walt

I'd do this. —Josh

let me know, I'm in, Sonja

Me too. —Lisa

Can not wait for this! Rio

Me too. Kathleen

Sounds like fun. If people are interested, I can bring some data sets to play around with. Alex

## Statistical Physics for Non-Physicists

Problem: Textbooks about this are written for physicists. Solution: A Physicist (or mathematician) that would be so kind and spend few minutes (or maybe hours) to explain all that stuff to people like me(Petr):-)

Ruben: Do you seek for a general introduction or something specific?

A crash course in Statistical Physics would be awesome. Let us know. — Carlos

I am interested too. (Soumya)

Me too. (Jean)

Interested! Meritxell

Interested! Giovanni

Ditto - Skyler

Me too. —Lisa

Me three. RobMills

I'd be willing to run such a tutorial. However, I would have to consult with some/all of the interested parties to find out what kind of statphys you want to learn about. There are a huge number of possible topics, one could start with basics like ensembles, or perhaps people are interested in master equation and other non-equilibrium techniques, or maybe critical phenomena is what people are interested in. I really do not know. (Orion)

Can you give us who are not physicists an introduction about a kind of special questions that you will think it from the viewpoint of physicists? Like complex network, dynamic, also something else, what is the most important measurement and dynamic process you want to observe? -Jiang

## Modern Logic and Reasoning

Like I mentioned in the 'ice-breaking', I could tell something about application of modern logic into human reasoning. It's a very board topic, and very new. Criticisms are welcome and needed. I would give some basic examples. On top of that, I would also say some development of logic, and how I found it useful in research, which might seem un-related to logic, esp. in social science. I am planning to give a 15 to 20 minutes presentation, UNLESS people want to hear more, in that case, please let me know. QiQi

I'm interested! Kathleen

Me too! Kolbjørn

Sign me up. — Josh

I'm interested too! (Flavia)

I'm in! srideep

I'm in too Giovanni

Count me in - Skyler

I'd be interested in this as well. Tanja

Sounds great - i'll be there. RobMills

Please remind by email or somhow.. and sign me up! Sonja

I am in Qi, But where? Rio

Update! Time at June 10th, 03.15 p.m. - 03.35 p.m. CSSS 2008 Santa Fe-Schedule

## Introduction to the Design and Analysis of Computer Experiments

How do you find "interesting" behavior when your computer model is too slow or the inputs are too many to try every possible combination? Using an Arctic sea ice simulator example, I will show you how modern statistical methods can help you explore your virtual world more efficiently. Check out this brief overview or a more technical paper about global optimization. Also see Gaussian Processes for Machine Learning for a list of available resources. Béla

## Genomics / Central dogma overview

It seems like some of you might be interested in an overview of the central dogma of molecular biology to non-biologists. This could be an 1h tutorial on the major actors of gene expression: nucleus, chromosomes, chromatine, DNA, RNA (tRNA, mRNA), proteins, polymerases, ribosomes, transcription factors, and eventually a quick intro to small, non-coding RNAs as a bonus. Although being a bioinformatician by training, I'm happy to leave the way if a "hard core" biologist wants to do this tutorial (Molly ?). Edit if interested! Jean

I'd be happy to attend a tutorial in 'genomics for idiots' -- Laura

Me too. I am also interested in metagenomics if this is not too much of course. -- Francois

I'd like to go to a 'genomics for idiots' tutorial as well. -- srideep

Ok, so I'll prepare some slides. How about Monday 9th, 5p - 6p (location TBA) ? -- Jean

## Artificial Intelligence/Machine Learning

I (Nish) could introduce some of the basic methods in AI/ML. If there is significant interest in the two fields separately, I could do two tutorials. Would probably focus on the higher level, rather than the nitty-gritty details, as well as applications of the methods to real problems. I'm not necessarily an expert, although have a fair amount of experience in the area, so I would prefer a more interactive session, where questions can be answered by everyone.

Sign me up. — Carlos

I'm also interested. -Sarah

Me too! Flávia

How about "AI/MI for dummies", Nish? I've been wondering about it.... Rio

sounds good Riley_Crane

## A Crash Course to Classical and Evolutionary Game Theory

Game theory is the study of interactive decision making. Classical game theory aims to develop a general theory to describe how rational agents interact strategically. In many cases humans lack the kind of infinite computational power and time assumed by classical game theory. In the early 1970s the biologist John Maynard Smith introduced evolutionary methods to the field, dispensing with the assumption of hyper-rationality while changing many of the concepts central to the field along the way. The result was evolutionary game theory. This new framework has been used to model the behavior of fundamentally non-rational players (such as viruses) as well as humans.

In this tutorial, I'd try to introduce the basic concepts in both of these fields, namely, the definition of a game, payoffs, the Nash equilibirum and evolutionarily stable strategies, the replicator dynamics. I'll briefly mention the three basic classes of two-strategy games represented by the Prisoner's Dilemma, the Snowdrift Game (sometimes called the Hawk-Dove game or Chicken), and the Stag Hunt Game. Depending on particular interests of the group, we could prove the Bishop-Cannings theorem and give a classification of all symmetric two-strategy games; or look at updating methods and spatial chaos; reputation and image scoring; rock-paper-scissors in biological systems; or evolutionary branching and specialization.

If there's something else you'd like to know about EGT, shoot me (Josh) an email, and I'll see if I can dig up something I know on your topic. I'm not going to require any fancy mathematical background. If you've seen a 2×2 matrix before, great. Otherwise, it's not a big deal. We won't multiply them or calculate their eigenvalues. They'll just serve as a means for bookkeeping.

Note: Some of us are also thinking about setting up a working group as well.

Update: The next meeting has been scheduled for Tuesday, June 10 from 7–8pm in a location TBD.

### Lecture Notes

Lecture 1. Classical Game Theory

Please let me know about any typos, errors, or flat-out lies. Suggestions are good, too. Thanks.

- I'll sign up for this. Kolbjørn
- I'm interested too! (Flavia)
- I'll be there too. Kathleen
- I'm in. Jean
- I'm interested as well. Steve
- will be there at 3 Walt
- I'll be there, Petr
- Good stuff. I could also say a few things about adaptive dynamics, if there's interest. Sarah
- I'll be there. Jiang
- Count me in (Chris)
- I'm in. Tanja

## Resilience of social-ecological systems

The resilience perspective is increasingly used as an approach for understanding the dynamics of social–ecological systems. Essential for the resilience perspective is the recognition that living systems are not in equilibrium but rather in a domain of attraction. Many dynamic systems, however, have multiple domains of attraction. Moreover, self-organizing processes can create or change the shape and depth of this domain of attraction. Within the resilience perspective, new pathways of sustainable development can be represented by crossing a threshold from a domain of attraction and/or by creating new domains. Resilience is a measure of how much change or disruption is required to transform a system from being maintained by one set of mutually reinforcing processes and structures to a different set of processes and structures. If you are interested we (Mike and Dirk) can introduce you to some of the insights developed by the resiliance alliance and the challenges we face in understanding these kind of systems.

I am interested in this too. Richard

Very interested, any idea of when you will do it? Walt

I'm interested as well. Steve

I'm interested too. - Skyler

I think to contribute from my previous work on SES. Rio

## Introduction to classical control theory

I (Srideep) can offer a 'quick' tutorial on control theory/control systems. This is will be a simple introduction to the motivation, basic ideas, issues and jargon in the field. If you are interested, please let me know about your background in linear algebra, complex analysis and calculus. Depending on the background, I might spend more or less time introducing the field.

Ideally, if you know what eigenvalues and eigenvectors of a matrix are, what a pole of a complex function is and how the solution of a linear differential equation looks like, you are ready to jump right into controls. If the words above don't mean much at all, then we can run a quick 'review' of what they mean intuitively. you can sign up here or send me an email srideep

Update! Lets plan on discussing this early next week. Will fix up a time by the end of this week. Liz bradley will be done with her introduction to dynamics and the eigenvalue, eigenvector tutorial will be done this friday. This will make my life easier! :-)

I'd be very interested in this tutorial. I think I'm basically OK on the prerequisites, but I wouldn't be annoyed by a review. Perhaps Monday? -- Laura

I'm in too. I guess I should be ok on linear algebra, calculus and linear ODEs, but I don't know what the pole of a complex function is. Jean

I'm in. If we can start with 'pole' thing, that would be wonderful. - Masayoshi

Hi Srideep, please put me in this group. About my background on the subjects you asked; zero!!! Sorry. Rio

Definitely interested in this. - Jacob

I'm in. Paul

Looks cool. -Sarah

Me too! Rory

## Topology/algebra

I (Srideep) will also be happy to talk about topology, introducing the concepts of point-set topology. The language of modern mathematics is enshrined in the concepts of point-set topology. I can also talk about group theory and introduce abstract algebra to those interested. In my opinion, it is the most powerful gateway into abstract thinking. sign here or email me srideep

I'd be very interested in that. Jean

I'd be interested to see what you cover in the topology section. Algebra, however, is for the birds :) Paul

Srideep, can you do an introduction to category theory? Or would you be interested in co-organizing a tutorial with me? - Jacob

I'm very interested. Abby

Sounds like fun (Chris)

## Eigenvalues - what are they and how to find them?

I (Kolbjørn) can put together a brief and elementary introduction to eigenvalues and eigenvectors if anyone have an urge for this. Sign up or e-mail and we'll schedule something. Kolbjørn

UPDATE 06062008: SLIDES

UPDATE! Time: Friday June 6th, 01.00 p.m. - 03.00 p.m. If this collides with other stuff, please yell out! CSSS 2008 Santa Fe-Schedule

Yes please. Kathleen

I am also very interested Walt

I'm in as well Mark

Please - have always been kind of confusing to me. Jon

Let me in - Masayoshi

I'm also interested! Flavia

I'll be there. -Molly

I'm in as well. -Tanja

Me too! **Just to remind**; I think Classical and Evolutionary Game Theory (Josh)will be started at 3 PM. Rio

## How your computer works

Nish and Laura can give a joint tutorial on 'how your computer works'. What happens when I type 'www.santafe.edu' in my browser? How does a web server at santafe.edu handle all those incoming requests? What happens when I use a WiFi access point? Basically, we'd be happy to take your questions about how your computer works and do our best to answer them - we're also happy to have other co-tutors.

Let us know if there's interest Laura, we'd probably schedule later next week, to not conflict with tutorials that focus on maths and other project prerequisites.

I would love this. -Sarah

## How your hardware works

Along the same lines as the computer tutorial, I've found myself discussing hardware with a number of folks. And why hardware matters from a massive parallelism perspective (which is quite common in the complex research areas I've encountered). If folks are interested, I can give a rough overview of the way hardware works in different types of computers and supercomputers (as much as I understand of it) as well as how to best leverage that knowledge.

Not sure how this differs from the the one above it, but def. interested (Chris)

## Computational Physics for Non-physicists or A small introduction into Applied Physics

I've seen that many people are interested in physics. I could give an introduction to "computational" physics - this means physics with a PC. Actually, it is very broad and gives some basics for simulations (interesting for all simulation-folks):

- What is a 'random number generator' and why should I know something about it?

- What are Master-equations?

- The Ising-model / Voter-model

- The Central Limit Theorem or why does it make sense to average over multiple runs of a simulation?

- ...

I'm very interested Nish

I'm in too. Jiang

srideep is in. Sounds great. Molly

Looking forward to it. Petr

## Information Theory

An open discussion of Shannon information theory (would like some help in presenting this part clearly) and then some newer results from its application to cellular automata (and potentially other complex systems).

Interesting. I remember something from the master course I took. Giovanni

I'd love to participate. -Sarah

I'm interested.Paul

I'm in. --Lisa

I'm in. --Meritxell

FYI: Tom Carter is going to be talking about Information Theory a bit tomorrow from 2-3pm, not sure of a location yet, but its on the schedule.

## Cellular Automata

CAs (particularly ECAs) are a very interested model of computation. How do 8 rules (ECA 110, e.g.) emulate a Turing Machine? Why is that interesting? What can we learn about what defines computation given CAs? Maybe we can also discuss some simple computational (Turing) theory.

I'd go to that twice. —Josh

Sounds like fun. Chris

## A little analytical tool-box: Non-linear dynamics, ODEs, PDEs...

The Brothers Foster would be happy to offer some tutorials on analytical methods. Depending on what Alfred Hubler covers, we can do some fraction of Strogatz (flows on the line & circle, bifurcations, maybe linear systems, index theorem, etc.), as well as offering a basic introduction to solving linear ODEs (no theorems, just techniques) and simple PDEs like the heat equation, with boundary conditions. Ideally this would come after Kolbjørn's eigen-stuff course, so we can just assume familiarity with that.

We've put a tentative time for our tutorial on the schedule: June 16 at 3:15pm. Let us know if this doesn't work out for some reason and we can try to change it.

These are fun topics! I never get enough of them! -- srideep

Sounds great. Molly

Interesting -- sure. Lisa

Very useful! Kathleen

Need this.... Rio

I'm in! Flávia
great! Riley_Crane

Brothers Foster rulez! I'll be there. Petr Count me in! Giovanni

## Linguistics

Can someone (I don't know who) perhaps offer a tutorial on basic linguistics stuff? I am particularly interested in generative grammar and coverage of the Chomsky "Three Models" paper, but maybe there are more interesting topics to be discussed these days... -Jacob

I could easily do a Saussure/Pierce tutorial, along with how this has been applied from everything to kinship structure to film theory to table manners, but this is continental structural linguistics, very diff from the chomsky stuff. I think Peter Graff can do the chomsky stuff, though, perhaps we could work on this together (Chris)

Would love both tutorials. Esp. the kinship structure stuff (is this Andre Weil's algebra chapter on kinship, from Levi-Strauss I think?) -Jacob

I'd love to participate. -Tanja

## Fitting models to data

A few people have asked me for a brief review of fitting models to data, but I'd like to know what methods interest you. I could start with least squares and progress to Bayesian approaches, maximum likelihood, and some more recent developments in methods for exploring space (GAs, particle filters, MCMC) with which I'm familiar. I'm by no means an expert in all these topics, so please add your name below if there's something you'd like to learn about (a particular method or method for a particular context) or teach. I feel like this tutorial would be most appropriate for the third or fourth week. -Sarah

I am really interested in this. (Soumya)

cool Riley_Crane

## Networks, Sign Systems, and the Mind

So, as an outgrowth of the (continental) theory/philosophy working group, I've come up with two ideas for tutorial/discussion sessions on stuff people might be interested in, in which I'd likely throw some materials at the group, then see where discussion takes us. The first one would be on theories of language and the mind. Probably start off with the first real theory of language and the brain, Freud's topological theory, and then move to how this was absorbed into structuralist linguistics/semiotics in the 1950's (Saussure's theory of signifiers, Jakobsen on axes of discourse, paradigms/syntagms, metaphoric value transfer, and how this was applied to kinship structures, social institutions, etc.) From there we could look at how Jacques Lacan built upon this with his 'mathemic' algebraic notation for discourse analysis. We could then look at how networked theories of mind challenge both the Lacanian model and its American counterparts (Fodor's psychosemantics, for example), particularly in regard to connectionist architectures in artificial neural networks, and how this leads to more distributed notions of linguistic structure. These new paradigms can allow us to move beyond notions of discrete 'signs' existing somewhere in the brain to models based on research in microfeature maps, dynamic network synchronization, spreading activation, and feature vectores. When synthesized with Lacan's insights, and blended with some ideas from object-relations theory and by thinkers like Marvin Minsky and Gerald Edelman, its possible to come up with models that actually reflect the impact of complex systems theories. Likely wayy too much stuff to squeeze in, but certainly enough to get a conversation going, even if we don't get to half of it!

Anyone interested? (-Chris)

## Questions at the Intersection of Neuroscience and Complexity

Update! This tutorial is scheduled for 10:30 AM Wedenesday (June 11), in the

small library on the upper floor of Petersen student center, just behind the main conference room.

Related to Chris' proposal above, but perhaps on the flip side, I'd be happy to give a tutorial / lead a discussion on issues where questions of complexity intersect with problems in neuroscience. I'll distinguish this topic from the idea above, in that I'll focus a bit more on bottom-up questions rather than purely theory-motivated questions. Neuroscience is a very large field, so I'll talk about some of the things I know, but encourage others to bring their own knowledge and curiosity.

I'll start with a short background on neuroanatomy of humans and other species. Then I'll do a survey of what's sometimes termed "systems neuroscience". This is the branch of neuroscience that asks about behavior roughly on the level of neural circuits -- but which often jumps up and down scales, and overlaps pretty significantly with ideas in "cognitive neuroscience" where the focus is on a lot of the interesting, higher-order behaviors unique to relatively few species. Then I'll go over a couple of papers which I think start on a road to using complex systems. Examples of what I might talk about would be:

- Kiani et al J. Neurophys 2007
**Does the visual system naturally group objects into heirarchical categories?**These authors tried to apply some dimensionality reduction techniques to neural data from monkey inferotemporal cortex. The ideas from Dr. Newman's lectures may be very appropriate here. - Assisi et al. Nature Neuroscience 2007
**Sparseness in representation of odors**. The Laurent lab has been combining high-quality experimental methods in the insect olfactory system with computational models (including network models) to look at how the insect system (and more recently the mammalian system) represent odors. The system presents a very interesting contrast to the visual system, in terms of the sparseness of representations at the early levels. There's some elegant circuitry mapped out here.**BONUS QUESTION!**I remember one of the questions they investigated earlier was how locusts transition from 'happy grasshopper' mode to 'Biblical swarm' mode. This has something to do with olfaction. This population behavior is probably a very intersting bifurcation; we can dig into what this reflects. - Machens and Brody, Neural Computation 2008. [Carlos Brody] does a lot of work on how neural circuits dynamics can allow for short term memory behavior. This includes comparing a perceived sensation to something you experienced a few seconds or minutes ago, and constructing an internal sense of how time elapses. His group uses tools like attractor networks to model this behavior.
**Walter Freeman's work**. Freeman studies the mammalian visual system, but also has a background in talking about how neural circuits encode meaning. This will be an opportunity for me to go back and find some interesting results to discuss. We may also highlight the questions of information theory and oscillatory behavior in neural circuits, which covers researchers like Pascal Fries, John Huguenard, and David McCormick. I'll update this part with a more specific paper when I find a good one.

**Timing?** Right now I'll focus on Wednesday morning, June 11. Please let me know below if you're interested. If it's a small group we can meet in the small library next to the main room; this might encourage discussion. And of course, let me know if there's something within this area in which you're more or less interested.

Cheers, Rory

I'll be there Wednesday AM. Teach me, oh wise Neuroscientist! Nish

Hellsyeah. Chris

## Network Economics and Value Theory

So, for the third week of CSSS, I'm thinking of maybe doing a session on 'Network Economics and Value Theory' for whoever's interested. Likely start off with Marx's three levels of value (use, exchange, surplus), move to his theories on production, formulas for capital, commodity fetishism, sticky points of his famous 'labor theory of value,' then on to his analysis of modes of production, and his thesis on the falling rate of profit that was supposed to bring down capitalism (but which obviously didn't). From there we could discuss critiques/updates of this theory via the growth of Keynesianism/Stalinism/Neoliberalism, in order to get to David Harvey's new work on how neoliberal economies largely avoid demand crises by engineering carefully managed accumulation crises whose effects can be easily passed off to poorer nations using multi-national postwar institutions like the IMF/WTO. This leads to examples of how networked models can help us understand today's economic crises (for example, how evolutionary search models can help us understand the ways in which 'overleveraging' economies via 'market derivatives' can help funnel capital to hedge funds in rich countries). From there we could look at critiques of economic theories of value, particularly Deleuze and Guattari's notion of 'desiring-production' as that which links production of commodities to the production of consumers by the social unit of production, namely, the family, and how even this model needs to be rethought in terms of shifts in mass media. Other topics could include theories of network political activism, namely those of Hardt and Negri (Empire/Multitude) and Ernesto Laclau on social dislocations and crisis management via counterhegemonic blocs.

Anyone interested in any of this stuff, lemme know! (-Chris)

## Topological and Symbolic Dynamical Systems

I would like to address the perceived interest among few of us here in topics relating to the topological dynamics and symbolic dynamics. I can talk a bit about ideas relating to the topological properties of dynamical systems and systems with very little structure to them (i.e., systems whose state spaces are merely a hausdorff space and a dynamic shift which is a continuous function). The symbolic dynamics part will deal with spaces of sequences of symbols and the dynamics being a shift map. I would like to wrap things up with a powerful tool - topological conjugacy - which allows us to define an 'equivalence' between two dynamical systems, one of which might be easier to understand and analyze. Ideally, this discussion will come after my topology tutorial, but I'll spend a few minutes describing formally and intuitively, the terms I use. Alternatively, we can form small discussion groups and chat about this over a cup of tea. srideep

absolutely interested. Chris

Interested! Giovanni

## Economics & Finance 101

A 1 hour mini crash-course on the basic principles of Economics and Finance. The aim of this tutorial is -hopefully- to give a heads up for the upcoming Economics/Finance week for people who do not have a background in Economics. I will introduce 3 simple models of microeconomics, macroeconomics and finance that can give an idea of what economists do. Carlos

**Date and time:** Friday June 13, 3:00-4:00pm.

**Note:** Reply to this page if you are interested in taking this tutorial.