Joel Stein has an truly atrocious piece in Time magazine, which opens with
I am very much in favor of immigration everywhere in the U.S. except Edison, N.J.
I can see how Stein is sort of trying to be funny, but the whole piece has a stink (like uncooked hing) about it that got Anna up in arms and Mimosa writing:
But really, what bothers me about this piece, why it didn’t strike me as satire, is that it seems to assume that there really is a dominant narrative out there, i.e. that “white” culture is where it’s at. Assimilation is not an option, it’s a requirement for these rude new aliens – but of course, that assimilation is on the dominant narratives terms.
Klein’s response:
Didn’t meant to insult Indians with my column this week. Also stupidly assumed their emails would follow that Gandhi non-violence thing.
Perhaps he thought the emails would also be curry flavo(u)red?
On that note, here is a quote from Amitava Kumar’s Passport Photos, which I am enjoying right now:
If the word ‘curry’ doesn’t have a stable referent or a fixed origin, how can its changing use by postcolonials be seen as a sign of resistance?
called the symmetrizability of the channel such that for list-decoding with list sizes 
the capacity is 0 and for larger list sizes the capacity is the randomized coding capacity of the AVC. This work extended this to the multiaccess setting, which is a particularly tricky beast since the capacity region itself is nonconvex. He showed that there is a 
such that the capacity region has empty interior if the list size is 
and that for list sizes 
you get back the randomized coding capacity. What is open is whether the list sizes for the two users can be different, so that this gap could be closed, but that problem seems pretty hard to tackle.
based on 
, where 
is the blocklength and 
is the delay parameter. Suppose everything is binary and the adversary gets to flip a total of 
bits of the codeword but has to see it causally with delay 
. If 
the adversary sees nothing and the average-error capacity is 
bits. If 
the adversary can do a lot worse and the capacity is 
bits. What we show is that for any 
we go back to 
regular graph will be a very high quality expander (for very small sets) and therefore a (very small) constant fraction of bit-flipping errors can be corrected by 
check nodes, if we take 
to be the incidence matrix of the bipartite graph (the parity check matrix of the code), we can form 
and look at its eigenvalues
and Tanner’s spectral bound on expansion is that expansion 
is greater than
for any size of expanding sets $\alpha$. Unfortunately this bound cannot certify expansion for any 
, which is exactly the point where it starts being useful for coding theory. Perhaps there are stronger spectral bounds that could establish more expansion, the book 
girth with high probability. When we actually tried to find a proof for this, for example looking at the 
probability. This is what is refered to as ‘locally-tree like’. I do not know of any stronger statements but I think it can be easily shown that for any fixed cycle length, the expected number of cycles of that length is constant for regular random graphs.
bipartite expander graphs. But given a fixed measurement matrix how do we certify that it is good and should be implemented in a system?
measurements one recovers almost all sparse signals of size up to $0.05 n$ (whp over supports) and the 
measurement matrix has 
non-zeros. (see our recent 
i.i.d. individuals with characteristics distributed according to 
and features 
conditioned on the individuals according to 
. The identification problem is this: given a noisy feature vector 
generated from a particular individual 
retrieve the index of the user corresponding to 
, so they are trading off identification and distortion. The solution is to code 
of 
features and the 
. So, as they put in the paper, “the primary contribution is demonstrating the equivalence between the database privacy problem and a source coding problem with additional privacy constraints.” The notion of utility is captured by a distortion measure: the encoder maps each database to a string of bits 
. A user with side information 
can attempt to reconstruct the database using the a lossy source code decoder. The notion of privacy by an equivocation constraint:
distributed sources and they want to create a good erasure code in a network: a data collector who accesses any 
system is storing incorrect equations. These could be originating from bit-flipping errors in the storage medium or (more likely) if a malicious node was injecting errors during a previous repair in the storage system.
and only send the projections. The error detection works since the projected data follows the same 
using a small seed 
, and project on that. All the storage nodes need to share the small seed 
.
where 
is the total variation bound obtained from the pseudo-random generator.
nodes in an 
(sometimes also found as 
in the literature) one can use an 
, encode into 
) and store each packet into a storage node. The reliability achieved is that any 
failures without losing data. But most of the time we only have one failure. We then want to repair this failure by creating a new encoded packet by communicating as little information as possible from 
. Another issue is that one can reduce this repair bandwidth if the storage per node 
is allowed to increase and there is a tradeoff involved.
.
of failed nodes. The second result in this paper is that all the other interior points of the tradeoff curve (except the points of minimum repair and minimum storage) cannot be achieved with linear codes for exact repair. ( Of course this does not preclude the possibility that they can be approached infinitely close by making the code packets smaller and smaller).
if the number of nodes helping for the repair is sufficiently large 
, the MSR cut-set point can be achived for exact repair. For this regime the paper presents explicit code constructions that use a small finite fields and build on 
regime. The paper uses the symbol extension technique introduced in the Cadambe-Jafar paper ![[0,A]](https://s0.wp.com/latex.php?latex=%5B0%2CA%5D&bg=ffffff&fg=333333&s=0&c=20201002 "[0,A]")
in which 
. The decoder hears noise when the encoder is silent, and furthermore doesn’t know when the encoder starts transmitting. They both know 
, however. They do a capacity per-unit-cost analysis for this system and give capacity results in various cases, such as whether or not there is is a 0-cost symbol, whether or not the delay is subexponential in the number of bits to be sent, and so on.
you get a central limit theorem (CLT). What if you normalize by 
for example? It turns out you get something like
is the rate function for the Gaussian you get out of the CLT. This is useful for error exponent analysis because it lets you get a handle on how fast you can get the error to decay if your sequence of codes has rate tending to capacity. They use these techniques to show that for a sequence of codes with gaps 
to capacity the error decays like 
, where 
is the dispersion of the channel.
. These give matching scalings up to the first three terms as 
. The first term is 
. Interestingly, with feedback, they show that the first term is 
times the term without feedback, which makes sense since as the error goes to 0 the rates should coincide. They also have a surprising result showing that with energy 
you can send 
messages with 0 error.