Thursday, December 14, 2017

Statistical properties of networks

Today I am giving a cake meeting talk about something a bit different. Over the past year or so I have tried to learn something about "complexity theory", including networks. Here is some of what I have learnt and found interesting. The most useful (i.e. accessible) article I found was a 2008 Physics Today article, The physics of networks by Mark Newman.

The degree of a node, denoted k, is equal to the number of edges connected to that node. A useful quantity to describe real-world networks is the probability distribution P(k); i.e. if you pick a random node it gives the probability that the node has degree k.

Analysis of data from a wide range of networks, from the internet to protein interaction networks, finds that this distribution has a power-law form,

This holds over almost four orders of magnitude.
This is known as a scale-free network, and the exponent is typically between 2 and 3.
This power law is significant for several reasons.
First, it is in contrast to a random network for which P(k) would be a Poisson distribution, which decreases exponentially with large k, with a scale defined by the mean value of k.
Second, if the exponent is less than three, then the variance of k diverges in the limit of an infinite size network, reflecting large fluctuations in the degree.
Third, the "fat tail" means there is a significant probability of "hubs", i.e. nodes that are connected to a large number of other nodes. This reflects the significant spatial heterogeneity of real-world networks. This property has a significant effect on others properties of the network, as I discuss below.

An important outstanding question is do real-world networks self-organise in some sense to lead to the scale-free properties?

A question we do know the answer to is, what happens to the connectivity of the network when some of the nodes are removed?
It depends crucially on the network's degree distribution P(k).
Consider two different node removal strategies.
a. Remove nodes at random.
b. Deliberately target high degree nodes for removal.
It turns out that a random network is equally resilient to both "attacks".
In contrast, a scale-free network is resilient to a. but particularly susceptible to b.

Suppose you want to stop the spread of a disease on a social network. What is the best "vaccination" strategy?  For a scale-free network that will be to target the highest degree nodes in the hope of producing "herd immunity".

It's a small world!
This involves the popular notion of "six degrees of separation". If you take two random people on earth then on average one has to just go six steps in "friend of a friend of a friend ..." to connect them. Many find this surprising but, this arises because your social network increases exponentially with the number of steps you take and something like (30)^6 gives the population of the planet.
Newman states that a more surprising result is that people are good at finding the short paths, and Kleinberg showed that the effect only works if the social network has a special form.

How does one identify "communities" in networks?
A quantitative method is discussed in this paper and applied to several social, linguistic, and biological networks.

A topic which is both intellectually fascinating and of great practical significance concerns

This is what epidemiology is all about. However, until recently, almost all mathematical models assumed spatial homogeneity, i.e. that the probability of any individual being infected was equally likely. In reality, it depends on how many other individuals they interact with, i.e. the structure of the social network.

The crucial parameter to understand whether an epidemic will occur turns out to not be the mean degree but the mean squared degree. Newman argues
Consider a hub in a social network: a person having, say, a hundred contacts. If that person gets sick with a certain disease, then he has a hundred times as many opportunities to pass the disease on to others as a person with only one contact. However, the person with a hundred contacts is also more likely to get sick in the first place because he has a hundred people to catch the disease from. Thus such a person is both a hundred times more likely to get the disease and a hundred times more likely to pass it on, and hence 10 000 times more effective at spreading the disease than is the person with only one contact.
I found the following Rev. Mod. Phys. from 2015 helpful.
Epidemic processes in complex networks 
Romualdo Pastor-Satorras, Claudio Castellano, Piet Van Mieghem, Alessandro Vespignani

They consider different models for the spread of disease. A key parameter is the infection rate lambda which is the ratio of the transition rates for infection and recovery. This is the SIR [susceptible-infectious-recover] model proposed in 1927 by Kermack and McKendrick [cited almost 5000 times!]. This was one of the first mathematical models for epidemiology.

Behaviour is much richer (and more realistic) if one considers models on a complex network. Then one can observe "phase transitions" and critical behaviour. In the figure below rho is the fraction of infected individuals.

In a 2001 PRL [cited more than 4000 times!] it was shown using a "degree-based mean-field theory" that the critical value for lambda is given by
In a scale-free network the second moment diverges and so there is no epidemic threshold, i.e. for an infinitely small infection rate and epidemic can occur.

The review is helpful but I would have liked more discussion of real data about practical (e.g. public policy) implications. This field has significant potential because due to internet and mobile phone usage a lot more data is being produced about social networks.

Friday, December 8, 2017

Four distinct responses to the cosmological constant problem

One of the biggest problems in theoretical physics is to explain why the cosmological constant has the value that it does.
There are two aspects to the problem.
The first problem is that the value is so small, 120 orders of magnitude smaller than what one estimates based on the quantum vacuum energy!
The second problem is that the value seems to be finely tuned (to 120 significant figures!) to the value of the mass energy.

The problems and proposed (unsuccessful) solutions are nicely reviewed in an article written in 2000 by Steven Weinberg.

There seem to be four distinct responses to this problem.

1. Traditional scientific optimism.
A yet to be discovered theory will explain all this.

2. Fatalism. 
That is just the way things are. We will never understand it.

3. Teleology and Design.
God made it this way.

4. The Multiverse.
This finely tuned value is just an accident. Our universe is one of zillions possible. Each has different fundamental constants.

It is is amazing how radical 2, 3, and 4, are.

I have benefited from some helpful discussions about this with Robert Mann. There is a Youtube video where we discuss the multiverse. Some people love the video. Others think it incredibly boring. I think we are both too soft on the multiverse.

Thursday, December 7, 2017

Superconductivity is emergent. So what?

Superconductivity is arguably the most intriguing example of emergent phenomena in condensed matter physics. The introduction to an endless stream of papers and grant applications mention this. But, so what? Why does this matter? Are we just invoking a "buzzword" or does looking at superconductivity in this way actually help our understanding?

When we talk about emergence I think there are three intertwined aspects to consider: phenomena, concepts, and effective Hamiltonians.

For example, for a superconductor, the emergent phenomena include zero electrical resistance, the Meissner effect, and the Josephson effect.
In a type-II superconductor in an external magnetic field, there are also vortices and quantisation of the magnetic flux through each vortex.

The main concept associated with the superconductivity is the spontaneously broken symmetry. 
This is described by an order parameter.

The figure below shows the different hierarchies of scale associated with superconductivity in elemental metals. The bottom four describe effective Hamiltonians.
The hierarchy above was very helpful (even if not explicitly stated) in the development of the theory of superconductivity. The validity of the BCS Hamiltonian was supported by the fact that it could produce the Ginzburg-Landau theory (as shown by Gorkov) and that the attractive interaction in the BCS Hamiltonian (needed to produce Cooper pairing) could be produced from screening of the electron-phonon interaction by the electron-electron interaction, as shown by Frohlich and Bardeen and Pines.

Have I missed something?

Tuesday, November 21, 2017

How do you run a meaningful and effective consultation?

It is now quite common for university management and funding agencies to run "consultations" where they interact with members of the "community" and "stakeholders". An example, I recently attended at my university was one concerning the university developing a "Mental Health Strategy".
Some departments run "retreats" for staff members with similar aims.
For reasons I describe below, I think such events vary greatly in their value and effectiveness.

I write this because I would like to hear from readers what they think are important ingredients for an effective and meaningful consultation.

My interest is partly because my wife and I were asked by a NGO and a philanthropic organisation to facilitate several consultations with a view to future grant-making initiatives.
My literature search for "best practises" did not yield much.
But here are two resources we did find helpful.

How Employees Shaped Strategy at the New York Public Library
[Published in the Harvard Business Review]

Appreciative Inquiry

Both of these focus on finding a balance between "bottom-up" rather than a "top-down" approach.
They focus on positive things that may be already happening and building on them rather than focussing on problems.

A while ago I heard a talk by a faculty member who previously was Chief of Staff for a state Governor. He mentioned that one of worst things he had to do in that role was to run community "consultations" about "proposed" new government initiatives and policies. Unfortunately, the government had already made a decision but was merely conducting these events to give the appearance of consulting people who would be affected. A sad thing is that some would consider that Governor was one of the best that the state has had.

In a blog post, Best practice of top academic departments, Rohan Pitchford from the ANU School of Economics laments that in Australian universities
Over the last 15-20 years academic school meetings have gone from rambling and unstructured brawls to dull “executive infomercials”. The former led to marathon meetings. The current model has led to a middle-management culture that often does not take advantage of the very valuable specialists skills of talented, highly trained (and experienced) scholars in the department. Nor does it allow for reasonable checks and balances on the powers of the executive–something that is vital for the management of any group of academics.
Australian indigenous communities face many challenges. I recently heard one of their leaders say they were so sick of "white fellas" coming and running "consultations" aimed at finding "solutions" to their problems. He said the negative focus was actually dis-empowering the community, sucking away the energy and confidence to address their problems. They needed a more positive approach that focussed on some of the good things that they were doing and how they could build on those.

Here are a few things I have observed.

First, rearrange the furniture. This says a lot about the power  and communication dynamics in the room. A traditional lecture theatre means people can't see each other and that everyone is looking at the "presenter" who has the power and presents pre-packaged solutions. In contrast, a flat floor with groups of people around circular tables which are used for break out discussion groups, suggests something quite different. My wife taught me this. I also heard from Jenny Charteris (who does this for a living) that this is the first lesson of Facilitation 101.
It was interesting that the UQ Mental Health consultation was done in a good room like I describe above and I think this did facilitate more discussion, including after the meeting. I don't know if this was by intent or whether it was just the room that was available.

Second, it is important that people are heard and feel heard.
In many Australian universities, staff surveys have shown that the vast majority of staff say that "senior management does not listen to other staff". I have also seen instances where someone up the front exhibited what seemed "fake empathy". "I hear you, but ...." and later implemented policies that were contrary to what happened at the meeting.

Third, allow plenty of time for discussion, both in small and large groups. It is also to break up the small groups along different demographic lines.

Fourth, interaction both before and after any meeting is valuable. This also means providing different forums and means of communication, from anonymous comments on a website to public discussions with large groups. I thought it was good that for the UQ Mental Health consultation they said they had already run some small focus groups to get ideas.

What do you think are important ingredients for a meaningful and effective consultation?

Monday, November 20, 2017

I am not that Ross MacKenzie

Today the Australian Medical Journal published an article

Legal does not mean unaccountable: suing tobacco companies to recover health care costs 
Ross MacKenzie, Eric LeGresley and Mike Daube

This is getting some press and community attention.

For the public record, I am not one of the authors. I am Ross McKenzie.

Yesterday, I got an invitation to do an interview with a radio station in New Zealand!
Now, I just received the following hate mail.
Pity that you don't advocate for the government to recoup alcohol costs from companies, who have caused much more damage to drunks and others, you intellectual pigmy

Monday, November 13, 2017

Two important principles of time management

1. Delegate

2. It can wait.

These are also conducive to good mental health.

The second is not a mandate for procrastination.
Rather it is a mandate to be pro-active rather than reactive, to set and stick to priorities, to not let the squeaky wheel get the most oil, to let people solve their own problems,  ....

I often feel pressure to get a long list of things done as soon as possible. This is not good for my stress level and mental health. However, if I can calm down and let things go, and come back to them later, I will have a better sense of perspective.

I don't claim to have the best time management. Some earlier thoughts are here.

Tuesday, November 7, 2017

Social qualities emerge from multiple interactions at multiple scales

Different qualities are used to describe and characterise societies: civil, fair, intolerant, racist, corrupt, free,  ….

Two big questions are:

How does a society make a transition between from a bad quality and a good quality?

What kind of initiatives can induce changes?

Initiatives can be individual or collective, political or economic, local or national, ...

For example, how does reduce corruption, which is endemic in many Majority world countries?
Or in the USA, why is public debate losing civility?

I think it is helpful to acknowledge the complexity of these issues. They have some similarity to wicked problems. They are problems that involve multiple interactions at multiple scales. Some of these interactions are competing and frustrated (in the spin glass sense!) and initiatives can lead to unintended consequences.

Whether you look at societies from a sociological, cultural, geographical, political, or economic perspective they involve multiple scales. For example, at the political level, one goes from local to city to state to national governments to the United Nations. In some countries corruption (bribes, extortion, nepotism, tax evasion,…) occurs at all levels. A policeman demands a bribe for a traffic violation. A university administrator changes records so his nephew, a mediocre student, can be admitted to medical school. The president of the country moves millions of dollars in foreign aid money into an off-shore bank account….
These phenonmena occur at multiple scales and involve multiple interactions. For example, an individual citizen will interact with many levels of government, and government agencies, and with each may be involved or impacted by a corrupt interaction.

Civility (respect, graciousness, politeness, listening) or uncivility (disrespect, rudeness, contempt, shouting) also occurs at many levels. These range from everyday conversations, comments on Facebook, to debate in parliament, to the Twitter feed of the President of the USA.

Michel Foucault, is one of the most influential (for better or worse) scholars in the humanities from the 20th century. He is particularly well known for his arguments that power operates at many levels and in many different ways in societies.

I find a multi-scale perspective helpful because it undercuts two extreme but common views concerning how we address significant social problems.
One view is the “top-down” perspective that if we just have the right national leader and the right laws a problem will be solved. This is argued for a whole range of issues ranging from corruption to sexual harassment, to “hate speech”.
The other extreme is the “bottom-up” view that the problem can be solved by individuals just making the right choices. Each individual should be polite to others and not give or take bribes. We need both approaches.

Moreover, I believe we need initiatives at all levels and interactions.
The importance of the absence of the intermediate scales (and the associated concept of social capital) was highlighted in Bowling Alone: The Collapse and Revival of American Community, by the Harvard political scientist Robert D. Putnam.
An example of a multi-scale perspective is in the Oxfam book, From Poverty to Power: How active citizens and effective states can change the world.

A question that is both practically important and intellectually fascinating is:

What are the critical parameters and their values at which a society undergoes a “phase transition”?

Such a question is addressed in
The Epidemics of Corruption 
Ph. Blanchard, A. Krueger, T. Krueger, P. Martin

The figure is from a paper, Small-World Networks of Corruption.