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Siddhartha Gadgil
Works at Indian Institute of Science
Attended California Institute of Technology
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Angular dart with server sent events (or websockets)

I was trying to use angular dart with websockets/server sent events and could not find any documentation/examples (there are some for angularJS but that seems very different for such things). A few things I tried also did not work.

Does anyone know how to do this?

P.S. Also posted on SO
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Firstly, my question was answered on SO.
There are many examples of websockets, and I have used them before. My question was concerning with combining them (actually Server Sent Events) with AngularDart. In case others are interested, here are the problem and solution:
(1) In using without angular, I created  an EventSource objects, gets an Event Stream using onMessage and used its listen method to change some variables (with the .. this was actually just one statement).
(2) In angular I had to change a field of a constructor, so I tried to make the statement creating and binding the EventStream a field definition in the controller. This is not permitted.
(3) What works is to make this statement part of the constructor (following the SO answer).
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Looks very good, but can you share some code? I am struggling to do the same (have used dart a bit, but not the javascript interop). 
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Blog moved: Logic, types and spaces

I have moved my blog, with some rewriting, from Wordpress to _Octopress on Github pages" (the new link is below).

This gives me better (both easier and better rendered) latex support (both inline and display mode, via mathjax) and better support for embedding code (once I pretend Agda code is Haskell). I also now have local text based sources from which the site is generated.

The only cost of the move was a little bit of initial setup required. There are plenty of instructions around, which almost worked, but with a little glitch - some commands in both my setups (Windoows 7 and Ubunutu) said that I did not have enough permissions. The solution was obvious in Ubuntu (use sudo). It turns out that in Windows 7 an equivalent way is to right click on the shortcut to the terminal (I use powershell) and run as administrator.
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New post: Logic from type theory
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Yes, my blog. What I am teaching (from Jan 2014) is more of a pre-HoTT course - since I plan to not assume much background or sophistication (i.e., accessible to undergrads) and include classical logic as well, I will probably do only the basics of HoTT.
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The work of Bhargava and the Birch and Swinnerton-Dyer conjecture

+Manjul Bhargava [1] is, in my mind (and many other peoples'), a top contender for a Fields medal later this year at the International Congress of Mathematicians in Seoul. A report on some recent work of his is here:

http://mattbakerblog.wordpress.com/2014/03/10/the-bsd-conjecture-is-true-for-most-elliptic-curves/

He has announced that the Birch and Swinnerton-Dyer conjecture [2] is true for at least (just under) 2/3 of all elliptic curves. This is an improvement of past results of his (and coauthors) in this direction (showing a 'positive proportion' satisfy BS-D), and a comment to the post indicates that this is expected to improve to 4/5 given some ongoing work by Chris Skinner and collaborators.

That this work is considered by many to be Fields medal-worthy is analogous to how Stephen Smale [3] and Michael Freedman [4] won the Fields medal (essentially) for their proofs of the Poincaré conjecture in dimensions 5 and above, and in dimension 4, respectively [5]; it wasn't the original big conjecture, but it shed light on the general problem and why proving it in dimension 3 (the 'real' Poincaré conjecture [6], eventually proved by Grisha Perelman [7]) was going to need completely different tools.

So what is the Birch and Swinnerton-Dyer conjecture? Essentially, it tells us something about the number of rational-number solutions to certain two-variable cubic equations in two variables, with rational coefficients, defining a so-called elliptic curve. Such curves are not ellipses, but there is an indirect historical link, via functions which calculate lengths of arcs on ellipses. If we look at solutions over the complex numbers, then one finds they form a surface looking like the skin of a donut (the one with a hole), possibly pinched or 'degenerate'.

However, if we look for solutions among the rational numbers a/b, with a and b whole numbers (and possibly b=0, corresponding to a 'point at infinity'!), then this is a lot harder, and then the problem falls into two cases: a finite number of solutions and infinitely many solutions. In the infinitely many solutions case, we can further distinguish the 'number' of solutions, in a manner of speaking, by the dimension, or rank, of the infinite part. (And the finite number of solutions in fact corresponds to rank 0.) The fact that this dimension is finite is a hard theorem all on its own, due to Mordell [8]. There is an algebraic structure on the rational solutions to the equation underlying an elliptic curve, namely that of an abelian group, and the animated gif below shows one way of thinking about this (source: http://en.wikipedia.org/wiki/File:EllipticGroup.gif). This algebraic structure means that the possible solutions are very constrained and there is a rich theory behind elliptic curves for this very reason (and this algebraic structure is why elliptic curves can be used for cryptography, including the infamous set with a built-in back door [9])

Now there is another way to calculate a 'rank' for an elliptic curve, which uses complex analysis, or more roughly, infinite products built from the elliptic curve. One defines a so-called L-function, similar in character to the famous Riemann zeta function [10] (but unrelated), and then the Modularity Theorem [11], proven in part by Andrew Wiles [12] on his way to proving Fermat's Last Theorem [13], tells us that this L-function makes sense for inputs other than when it was first defined, namely we can plug in any complex number and get a sensible result. If one analyses the behaviour of this function at the input 1, roughly how fast it grows heading away from that point, then this defines a non-negative integer called the analytic rank of the original elliptic curve.

That these two numbers, the rank and the analytic rank, have anything to do with each other, especially since the second one wasn't even defined for all elliptic curves until the late 1990s, is hugely surprising. Birch and Swinnerton-Dyer made their conjecture based on computer work in the early 1960s on elliptic curves for which the various quantities were known.

So at last, what is the conjecture? Namely that the rank and analytic rank are equal, and in fact there is a conjectured formula for the rate at which the values of the L-function associated to the elliptic curve increase as one heads away from the point 1 in the complex plane. This is terrifically scary, involving the size of the Tate-Shafarevich group Ш (one of the few, if only, instances of Cyrillic used internationally by mathematicians), which is mentioned in the linked blog post, the number of solutions in the 'finite part' of the elliptic curve (for those who know group theory: the order of the torsion subgroup) and other quantities which are associated to each elliptic curve.

Now the really interesting thing is that we expect most elliptic curves to have rank (either sort!) equal to either 0 or 1, and by 'most' I mean 100% of them. Thus 0% of elliptic curves should have rank bigger than 1. This may seem weird, but there are infinitely many elliptic curves, and so 0% really means something like 'given any tiny positive number t, then taking larger and larger samples of elliptic curves, I expect less than t% of them have rank bigger than 1'. And for the rank 0 and 1 curves, these are expected to be split 50-50 (the 'parity conjecture') between the two cases. The large-rank curves are indeed rare: the largest explicitly-known rank of an elliptic curve is 18, with cubic equation

y^2 + xy = x^3 − 26175960092705884096311701787701203903556438969515x + 51069381476131486489742177100373772089779103253890567848326,

due to +Noam Elkies, though there are examples with a rank at least 28, but with actual rank unknown. Interestingly, the 'finite part' of the elliptic curve (the torsion subgroup), can only be one of 15 things: the trivial group, the cyclic group C_n of order n=2,3,..,10 or 12, or the product of C_2 with C_2m for m=1,2,3,4.

To summarise: what Bhargava has done (with his collaborators) is show that in at least 2/3 of all elliptic curves, the rank and the analytic rank coincide, showing the BSD conjecture for this many curves, with a view to extend this to 4/5 of all elliptic curves.

[1] http://en.wikipedia.org/wiki/Manjul_Bhargava 
[2] http://en.wikipedia.org/wiki/Birch_and_Swinnerton-Dyer_conjecture
[3] http://en.wikipedia.org/wiki/Stephen_Smale
[4] http://en.wikipedia.org/wiki/Michael_Freedman
[5] http://en.wikipedia.org/wiki/Generalized_Poincar%C3%A9_conjecture
[6] http://en.wikipedia.org/wiki/Poincar%C3%A9_conjecture
[7] http://en.wikipedia.org/wiki/Grigori_Perelman
[8] http://en.wikipedia.org/wiki/Mordell%27s_theorem
[9] http://jiggerwit.wordpress.com/2013/09/25/the-nsa-back-door-to-nist/
[10] http://en.wikipedia.org/wiki/Riemann_zeta_function
[11] http://en.wikipedia.org/wiki/Modularity_theorem
[12] http://en.wikipedia.org/wiki/Andrew_Wiles
[13] http://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem

(Thanks to +Peter Woit for the link to Matt Baker's blog posting)
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Voevodsky on why homotopy type theory.

(Note on sharing: I found this in Google+ but in a post that was not shared publicly, so I could not reshare. I hope there are no objections to my sharing the  link to the article).
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Thick and fast they came at last, and more and more and more.

Logic, Types and Spaces: next post, this time mainly functional programming.
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Another post on Logic, Types and Spaces
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I have started blogging about basics of logic, (dependent) type theory, Agda etc. leading up to a bit of Homotopy type theory. This is partly to learn the stuff and partly as a companion blog to a course I am teaching next year.
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  • California Institute of Technology
    Ph.D.(Mathematics)
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Mathematics (Low-dimensional topology), but trying to make computers make my job obsolete.
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