gphilip
Joined 16 years ago
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Comment · 2 years ago
Comment · 4 years ago
> Adding one edge after the exact number of edges required to create a Hamiltonian cycle (number of edges equal to number of vertices) would appear to break the property.
A Hamiltonian cycle is a simple cycle (no repeated vertices or edges) that contains every vertex of the graph. If a graph G has a Hamiltonian cycle, then adding more edges to G will not make that cycle go away; it will still be there. So the property of "has a Hamiltonian cycle" is not broken by adding more edges.
As a simple example: consider the graph which is the cycle on 5 vertices. That is, the graph has 5 vertices, and is just one big cycle with 5 edges. This graph has a Hamiltonian cycle (the entire graph itself is one such cycle). If we add an extra edge to this graph, say between vertices 1 and 3, the original Hamiltonian cycle does not go away.
> How can there be a lower bound other than zero? However small the possibility, surely given an infinite number of cases, there are infinite possibilities of a particular structure being created.
The lower bound can be other than zero because they are looking at the threshold (probability) at which the probability of the object existing goes from "very low" to "extremely high". This is alluded to in the following quote:
"When edges are added to a random graph of N vertices with a probability of less than log(N)/N, for instance, the graph is unlikely to contain a Hamiltonian cycle. But when that probability is adjusted to be just a hair greater than log(N)/N, a Hamiltonian cycle becomes extremely likely."
(Note that I plucked the above probabilities out of thin air just for the sake of illustration, just to give you an idea of the form that these statements take. For the precise probabilities, please ask Google.)
> What does this mean?
See: https://en.wikipedia.org/wiki/Sunflower_(mathematics)
> This seems to suggest multiple Hamiltonian cycles in a graph, contradicting the earlier definition that every vertex must be connected.
This is no contradiction. There can be multiple Hamiltonian cycles in a graph. Consider the complete graph on n vertices; there are roughly n-factorial-many Hamiltonian cycles. Any permutation of the vertices corresponds to one such cycle. Different permutations can correspond to the same cycle, so the number is not exactly n-factorial. But you get the idea.
Comment · 5 years ago
I configured Fastmail to send emails that I compose from my work address, via the work SMTP server. Not any other type of email. And indeed, they don't send emails that I compose from my non-work addresses via my work SMTP server: they use their own server to send these.
The support person who is dealing with this also turned up the fact that this is a change that they made some time in 2019. Earlier to that, all emails from Fastmail Calendar were sent from the "[email protected]" address. They changed this in late 2019 so that Calendar now sends these mails from my work address (following some peculiar logic and email rewrite rules).
So yes, it is surprising that they send emails from my Calendar via my work SMTP server.
Comment · 8 years ago
It's "choline", not "chlorine".
Comment · 9 years ago
Here is one thing you could try:
1. Identify research scientists (e.g: in Google/IBM/Microsoft/... research labs) and professors (in institutes/universities) that you would like to work with.
2. Write to them directly, attaching your publications and requesting an internship.
Depending on how your publications are perceived, there is a good chance that at least a few will choose to engage with you.
Indian institutes funded by taxpayer money are required to follow a prescribed set of rules for selecting PhD candidates, in the interest of ensuring fairness, preventing nepotism, etc. . The competitive exams that you seem to loathe are part of this process, and professors can do nothing about this.
They have much more leeway in choosing interns, though. The rest follows as per kubrickslair's recipe.
Comment · 9 years ago
> You can also publish papers as an undergrad with your adviser's support in the US, is that not true in India?
It is just as true in India as it is in the US.
And: while it definitely helps if your college/department/advisor is there to lend you support, such support is not a prerequisite for getting published.
Comment · 9 years ago
I can speak of theoretical computer science: if you have work that is worth publishing (as evaluated by your peers), then yes, it is possible to publish without any affiliation. I would be very surprised if a good result is rejected just because the author is not affiliated.
(Indeed, it is possible to get published even if you have negative affiliation; see: http://insa.nic.in/writereaddata/UpLoadedFiles/IJPAM/20005a2... )
The operative word in the first sentence above is "if". In my opinion, unless you are in the Ramanujan or Erdős class, then it is highly unlikely that you come up with a publishable manuscript on your own. Briefly put: you need a lot of "context" to be able to do publishable work, and you are unlikely to get this context unless you interact with the research community.
You get shocked easily when you use the escalator.You wouldn't be electrocuted more than once.