## Profile

## Stream

### Brian Oxley

Shared publicly -**Place of Departure**

Chajnantor means “place of departure,” or more poetically “place of ascension” in the Kunza language of the Atacama region. It is a plateau about 5000 meters (16,000 feet) above sea level. Its elevation and arid climate makes for extremely difficult working conditions, but it also makes it perfect for the Atacama Large Millimeter/submillimeter Array, or ALMA.

ALMA is one of the first truly international astronomical endeavors. Rather than being spearheaded by a single nation with others lending primarily financial support, ALMA is a collaboration between the United States (NRAO), Europe (ESO), East Asia (NAOJ) and the Republic Chile. It’s coordination has been likened to the United Nations. Given ALMA’s 1.4 billion dollar price tag, international collaboration was the only way the project was feasible.

ALMA consists of more than 60 12-meter antennas as well as 12 7-meter antennas. The 7-meter antennas are designed to be closely spaced, forming the Atacama Compact Array (ACA). Since the antennas use interferometry to create images of the sky, the ACA creates a wide sky view, while the larger array of 12-meter antennas allows us to focus in on particular objects. The antennas can be moved to different locations to allow for different scales and resolutions.

The engineering of ALMA is incredibly ambitious. In order to combine signals from the antennas, as supercomputing correlator had to be built on the plateau. It is the highest altitude supercomputer on the planet. The correlator not only has to account for the arrangement of the antennas, but also the orientation of the Earth relative to the target object. As the Earth rotates, the effective separation of the antennas change. While this gradual change is a computing challenge, it also allows us to create a more complete image of objects.

Because ALMA focuses on millimeter wavelengths, it is perfectly suited to image cold molecular clouds, both in interstellar regions and surrounding young stars. Since it can image these clouds with the resolution similar to that of the Hubble telescope, it’s able to provide an incredible view of things like planets forming around other stars.

ALMA has only begun what is intended to be a 30-year mission to study the universe. As the largest international astronomy collaboration, it is perhaps fitting that it resides at Chajnantor, as it will likely be a place of departure toward some incredible astronomical discoveries.

This post was made possible in part by the ACEAP project, funded by the National Science Foundation.

### Brian Oxley

Shared publicly -On Flickr: https://flic.kr/p/uCqJna

Image Credit: NASA/JHAPL/New Horizons/Kevin M. Gill

### Brian Oxley

Shared publicly -**Why your friends, on average, have more friends than you do**

The

**friendship paradox**is the observation that your friends, on average, have more friends than you do. This phenomenon, which was first observed by the sociologist

**Scott L. Feld**in 1991, is mathematically provable, even though it contradicts most people's intuition that they have more friends than their friends do.

Wikipedia gives a nice intuitive explanation for this phenomenon:

*People with more friends are more likely to be your friend in the first place; that is, they have a higher propensity to make friends in the first place.*However, it is also possible to explain the phenomenon using graph theory and mathematical statistics. I give an outline of the mathematical proof at the end of this post for those who are interested, but the upshot is that if we look at everybody's numbers of friends, and these numbers have a mean of μ and a variance of σ^2, then the average number of friends that an average friend has is μ + (σ^2/μ), which will be greater than μ assuming that someone has at least one friend and that not everyone has the same number of friends.

The recent paper

*The Majority Illusion in Social Networks*(http://arxiv.org/abs/1506.03022) by

**Kristina Lerman**,

**Xiaoran Yan**, and

**Xin-Zeng Wu**explores some phenomena that are related to the friendship paradox. The authors explain how, under certain conditions, the structure of a social network can make it appear to an individual that certain types of behaviour are far more common than they actually are.

The diagram here, which comes from the paper, illustrates this point. It shows two social networks, (a) and (b), each containing 14 individuals. In each case, three vertices are marked in red; let's suppose that these correspond to the heavy drinkers in the group. In social network (a), the heavy drinkers are three of the most popular people, and the configuration of the network means that each of the other eleven individuals observes that at least half of their friends are heavy drinkers. This will lead these eleven people to think that heavy drinking is common in their society, when in fact it is not: only 3/14 of the group are heavy drinkers. In social network (b), there are the same number of heavy drinkers, but they are not particularly popular, and nobody in the group will have heavy drinkers as most of their friends.

Network (a) is experiencing what the authors call the

**majority illusion**, whereas network (b) is not. The illusion will tend to occur when the behaviour in question is correlated with having many friends. The paper shows that the illusion is likely to be more prevalent in

**disassortative**networks, which means networks in which people have less tendency to be friends with people like themselves. Observe that in network (b), many of the non-heavy drinkers are friends with each other, whereas in network (a), they are not. This suggests that network (a) is more disassortative, and thus more susceptible to the majority illusion.

The authors also study the phenomenon using three real-world data sets: (a) the coauthorship network of high energy physicists (HepTh), (b) the social network Digg, studying only the mutual-following links, and (c) the network representing the links between political blogs. It turns out that networks (a) and (b) are assortative, and (c) is disassortative. They also look at the the case of Erdős–Rényi-type networks, which can be thought of as random.

As the paper points out, the friendship paradox has real life applications. For example, if one is monitoring a contagious outbreak, it is more efficient to monitor random

*friends*of random people than it is to monitor random people. This is because the friends are more likely to be better connected, are more likely to get sick earlier, and are more likely to infect more people once sick. The reason for this has to do with the fact that these attributes are positively correlated with having many friends.

If you're wondering why your coauthors are on average cited more often than you are, or why your sexual partners on average have had more sexual partners than you have, now you know. I found out about this paper via my Facebook friend +Paul Mitchener, who has more Facebook friends than I do.

**Relevant links**

Wikipedia's page on the Friendship Paradox contains much of the information in this post, including a sketch of the proof given below: https://en.wikipedia.org/wiki/Friendship_paradox

Wikipedia on assortativity: https://en.wikipedia.org/wiki/Assortativity

Here's another post by me about the mathematics of social networks, in which I explain why it is impossible for everyone on Google+ to have more than 5000 followers. It provoked a surprisingly hostile reaction: https://plus.google.com/101584889282878921052/posts/YV7j9LRqKsX

A post by me about Erdős and Rényi's construction of the random graph: https://plus.google.com/101584889282878921052/posts/34guwy4ftWX

**Appendix: Mathematical proof of the friendship paradox**

Assume for simplicity that friendship is a symmetric relation: in other words, that whenever A is a friend of B, then B is also a friend of A. We can then model a friendship network with an undirected graph G, with a set of vertices V and a set of edges E. Each vertex v in V represents an individual, and each edge e in E connects a pair of individuals who are friends. For each vertex v in V, the number d(v) (the

*degree*of v) is the number of edges connected to v; in other words, the number of friends v has.

The average number of friends of everyone in the network is then given by summing d(v) over all vertices v of V, and then dividing by |V|, the total number of people. Using basic graph theory, this number, μ, can be shown to be equal to 2 times |E| divided by |V|, where |E| is the number of edges.

In order to find the number of friends that a typical friend has, one first chooses a random edge of E (which represents a pair of friends) and one of the two endpoints of E (representing one of the pair of friends); the degree of this latter vertex is the number of friends that a friend has. Summing these degrees over all possible choices amounts to summing d(v)^2 over all possible vertices, and since the number of choices is 2 times |E|, it follows that the average number of friends a friend has is the sum of d(v)^2 divided by 2 times |E|. Using the formula for μ above, it follows that μ times the average number of friends that a friend has is equal to the average value of d(v)^2. However, the average value of d(v)^2 is also equal, by basic mathematical statistics, to the sum of the

*square of the mean*of the d(v) plus the

*variance*of the d(v). The result follows from this.

#mathematics #scienceeveryday #spnetwork arXiv:1506.03022

### Brian Oxley

Shared publicly -### Brian Oxley

Shared publicly -### Communities

6 communities### Brian Oxley

Shared publicly -### Brian Oxley

Shared publicly -### Brian Oxley

Shared publicly -If you look 'into' it, can you work out the reflections?

It's not as good as I wanted, but lets me think about the next try. Next, I want to get interesting mathsy shapes and colour patterns in there.

I did something similar a couple of months ago. This time I'm going for a less abstract, and more realistic view. This one cheats a little, by increasing the amount of light that internally reflects, so that you get more reflections.

Lastly, once you see the face, you can't 'unsee' it :o)

- Rice UniversityPhysics, Music, 1987 - 1991
- Trinity UniversityPhysics, Music, 1985 - 1987

- Little Alchemy

- ThoughtWorksPrincipal Consultant, present
- Macquarie Offshore ServicesSr. Manager, 2013 - 2015IT Manager
- Macquarie Group LimitedSr. Manager, 2010 - 2013Java Architect
- ThoughtWorksOpen Sourcerer, 2003 - 2004Developer
- SimDeskSr. EngineerDeveloper
- NovasoftSoftware EngineerDeveloper
- Merrill-LynchContractor
- JPMorgan Chase & Co.Sr. Associate, 2006 - 2010Sr. Developer

In Gaza, entrepreneurs seek to create a tech hub www.gulf-times.com A pioneering startup accelerator is building businesses in one of the world’s toughest places |

Red-faced Pluto Full of Surprises www.universetoday.com Hey, Mars, you've got company. Looks like there's a second "red planet" in the Solar System — Pluto. Color images returned from NASA's New H |

Speech on the 150th Anniversary of the Declaration of Independence | Tea... teachingamericanhistory.org Philadelphia, Pennsylvania. We meet to celebrate the birthday of America. The coming of a new life always excites our interest. Although we |

Smaller Majority "Extremely Proud" to Be an American www.gallup.com This Independence Day, most in the U.S. are proud to be an American, including 54% who say they are "extremely proud" and 27% who are "very |

Evidence for stable room-temperature skyrmions www.sciencedaily.com Researchers have identified a class of materials that displays clear evidence for stable skyrmions at room temperature and above, paving the |

Iogro | LOTRO Players lotroplayers.com May 15, 2015. Hail and Well Met Friends! When we left off on our last episode, we had just seen the Kin Strife come to a boiling point and w |

Scientists mix matter and anti-matter to resolve decade-old proton puzzle www.sciencedaily.com Nuclear physicists have used two different methods to measure the proton's electric form factor. But the deeper that they probe inside the p |

xkcd: Bracket xkcd.com Warning: this comic occasionally contains strong language (which may be unsuitable for children), unusual humor (which may be unsuitable for |

A Casual Stroll through The Shire, Part 1 | LOTRO Players lotroplayers.com The Tolkien Professor Corey Olsen comes out of the starter area and starts Gryfflet, his hobbit burglar, on a tour of The Shire where he dea |

Mars Rover's Laser-Zapping Instrument Gets Sharper Vision www.jpl.nasa.gov Tests on Mars have confirmed success of a repair to the autonomous focusing capability of the Chemistry and Camera (ChemCam) instrument on N |

Physics Buzz: Physics in Verse: Maxwell's "I come from fields of fractur... physicsbuzz.physicscentral.com Here's another lovely bit of physics poetry. Last week it was John Updike on neutrinos. This week it is Scottish mathematican and physicist, |

Returns on Investments rememberingattention.blogspot.com If I buy groceries and provide a recipe, the teens can make dinner. In this case, the mushroom bisque from Cook's Illustrated, and roasted p |

Wide GOP field has party leaders anxious about ’16 - The Washington Post www.washingtonpost.com Officials fear a long primary battle will pull candidates to the right and drain their funds before the fall election. |

Andromeda and Milky Way Might Collide Sooner Than We Think www.universetoday.com The merger of the Milky Way and Andromeda galaxy won't happen for another 4 billion years, but the recent discovery of a massive halo of hot |

Generating compiler back ends at the snap of a finger | Lambda the Ultimate lambda-the-ultimate.org Ramsey and Dias have a series of papers about making it ever easier to generate compiler backends, and the claim is that they produce decent |

Morgan Group to build apartments atop Whole Foods Market in Houston's Mi... www.bizjournals.com The company developing the apartments also has a community on the very next block. |

In symbolic blow, Native Hawaiian panel withdraws support for world's la... news.sciencemag.org But Office of Hawaiian Affairs declines to oppose project |