Day 19 : The Giants!

Since I have been in bed most of the week, I finally put the kindle to good use and took up to reading.
Here, I'll try to put together a list of the various research I have read about so far, just to summarize the magnitude and depth of the rabbit hole. Here Goes

1. Barabási–Albert model
   This was the starting point for me, and quickly led me to the next checkpoint.
2. Scale-free network and Power-law decay
   Understanding these helped in gaining a better view  of the general idea behind the B-A model, and I can't say I wasn't surprised by the absence of the bell curve for a change.
3. Watts and Strogatz model and Small-world networks
   These models help generalise the idea a bit more, and now I realise what exactly is the difference in the scale-free network I aimed for, and the fat-tailed distribution I achieved.
   The achieved network classifies as small-world, while the targeted one should be a ultra-small world.

Extra Read :

1. Structure and Function of complex Networks - Newman

2.Scale-Free Networks are Ultrasmall - Cohen, Havlin

3.Introverts and Extroverts - Max Freyd

4. Biomarkers to detect All-Cause Mortality

Now time to go back to more scrambling, also, I started to look into Mathematica. It's fun!

So Long.

p.s. I'll keep coming back to add more useful and notable reads to this post.

Day 18 : Personality profiles

So it turns out our curve is but a part of a fat-tailed distribution, and this tail part very conveniently follows a power-law decay, which led me to believe free scaling was achieved. Alas!
After discussing this issue with my advisor, and several meetings with Maria, a friend from the behavioural science section, I am looking into personality profiles now, to modify the inherent attribute of the agents, with a focus on how people tend to be Introverts/Extroverts.
All the reading is keeping me away from coding for a while, but it is a fascinating area!
Hopefully I'll work up a base and modify the code by the middle of next week. So Long.

Day 17 : I Can Haz Plot!

After spending a week tweaking and tinkering, it finally looks better. I have the graphs for the frequency of of the agents with which they make connection. In simpler terms, this is what we get if we list all the values for NumOfConnections for the agents, and plot every unique value in this list against it's frequency in the list.

For a total (seeded as well as dynamically introduced) of 250 agents, the plot looks like

and for 500 agents, it looks like

Although not much clear yet, the constraint shows gaps, as I only let the agents connect for a strong probability (over 0.5) after modification with the belief values. Relaxing this criteria should fill up the gaps and give a more uniform graph, however, we can still see the hyperbolic nature of the graph.

Next To Do :

• Try for clearer presentation
• Code Cleanup - need to move the "makeConnection" module to a different script to remove redundant code.

Also, now it's time to get in touch with my advisor and treat myself to cake, maybe.

So Long.

Day 16 & a -half : Probability Modifiers Ahoy!

So, the additive probability modifiers are up.
They take the old BA- probability and modify them based on the distance in the belief values of the two agents in question.
Now I'll spend the next two days rechecking everything and trying to get some plots (stuck between histograms and scatter plots for now) to check if the network scales freely.
So Long.

Interesting addition : This post was originally from yesterday, but then I realised I was wrong in normalising the modified probabilities, so I went ahead and fixed it. 

Day 15 : B-A model

So finally the B-A model is up and running.
It can be seeded with N-agents, which make k -number of strong connections based on the distance in their belief factors, and then the user can dynamically introduce new agents to the scenario which form connections based on a popularity probability.

Now the work in progress aims to modify this probability for preferential attachment to account for the belief factors. So Long.

Day 14 : Back to Hack!

After spending a couple days designing and re-thinking what we have so far, and a meeting with the adviser, it's time to get coding again.
So, we already had enough features to generate a seed network, on top of that, now I have added the feature to dynamically add a new agent, keeping in peace with the concept of Continuous Growth mentioned earlier.
Then,  for a change of flavours, I plotted the numeric behaviour of the random-connected weak links, and for 150-500 agents, it's not really clear if they follow any pattern, and hence, no pretty graphs in today's post.

It's pretty late, and the bed is irresistible now. Implementing the rest of probability calculation will have to wait for another night. So Long.

Design 1 : Randomness Prevails

Having a seed network ready, I spent the past day and a half trying to mathematize (yeah, I just made it up) the "magic" mentioned previously.
After looking into logarithms, log-log, and logs of priors, (sudden obsession with logs, it seems, but they are kinda awesome), and some statistical pruning methods over the existing connections, it seems nothing makes too much sense, and hence I decided to go with the closest thing to magic, random functions.
So tonight, I'll start implementing the same. So Long.

In other news, Naiad goes into water tomorrow and can't wait for it. :)

Theory 1 : CGPA - Continuous Growth and Preferential Attachment

YAY! Theory time!! Okay, maybe not the best thing in the world, but important none the less.

As shown by Barabasi and team, real scenarios tend to follow a pattern for connection between nodes. But for all it's glory and charm, Math can never assure certainty, the best it can do is give you a probability for a connection to be formed. 

and then, with some magic, some connections are established

Something similar to this aforementioned "magic" is portrayed in the new series, Betas , nice timing, eh?!!
While one may argue that human connection is ultimately attributed to this 'magic' factor (others might use words like Charm, affection, courage, luck etc. ) , what math does is give us a tool to better understand what is happening, and peek into the how- and why- of it. 

The beauty of the model lies in the fact that it lets new nodes be a part of the network. "I don't need new friends, I have enough." - said no one ever.  This is what 'Continuous Growth' refers to.

Also, the part of the model about 'Preferential Attachment' says that heavily connected nodes are more likely to form new connections with an incoming node. In terms of a common man, it's like saying everyone at school knows the captain of the football team.

Keeping these two facts in mind, we'll focus on how hubs are formed around heavily connected nodes.

So now, I need to modify my existing model to act as a seed network and create a bigger network accounting for these two properties. Time to unleash the code monkey inside. So Long.

media courtesy : wikimedia. 

Reading 1 : H2H and communication

Found a really interesting article about H2H. It gives some ideas about the communication. Though it's still in design phase.