## Have any problems in pure mathematics been solved using artificial neural networks?

Neural networks are widely used to solve a variety of problems such as regression, classification, compression on data types ranging from numerical data to images to text. A recurrent neural network was even trained to write its own (mostly gibberish) mathematical proofs.

Has anyone successfully applied neural networks to solve any problems in pure mathematics?

## I stuck on the network’s settings with Griddb on my ubuntu

Hostname -i

I got 127.0.1.1

with this command `ip -f inet -o addr show eth0 | cut -d' ' -f 7 | cut -d/ -f 1`

I got Device "eth0" does not exist

So what do you suggest to fix it? or should I continue to use the ip 127.0.1.1?

## computer networks – Is e-mail communication peer-to-peer?

In his networking textbook, the world-renowned computer science expert Tanenbaum says that e-mail communication is inherently peer-to-peer. Here is the paragraph from the book:

Peer-to-peer communication is often used to share music and videos. It
really hit the big time around 2000 with a music sharing service
called Napster that was shut down after what was probably the biggest
copyright infringement case in all of recorded history (Lam and Tan,
2001; and Macedonia, 2000). Legal applications for peer-to-peer
communication also exist. These include fans sharing public domain
public software packages. In fact, one of the most popular Internet
applications of all, email, is inherently peer-to-peer. This form of
communication is likely to grow considerably in the future.

I have come across several people claiming the opposite – e-mail is not peer-to-peer. They say that there is no direct connection between peers. Also, one of their argument was that if you bring one of the servers down, e-mail won’t work anymore. However, logically, if Alice sends an e-mail to Bob, in my eyes, Alice and Bob are peers. Just as with regular (snail) mail, anybody can send an e-mail message to anybody. There is no distinction between clients and servers. Hence, logically, a simple two-party e-mail message is a message between two peers. The route the message traverses is irrelevant.

So, is e-mail peer-to-peer? If not, what did Tanenbaum mean by saying that?

## I have a networks question about slotted aloha protocol

ii. 500 users are competing for the use of a single slotted ALOHA channel. The average
user makes 72 requests per hour. A slot is 100 μsec. What is the approximate total

## graphs and networks – How to extract the adjacency matrix associated with a subgraph defined by FindPath

For a directed graph `g`, one can obtain its adjacency matrix as:

``````SeedRandom(3);
g = RandomGraph({10, 20}, DirectedEdges -> True, VertexLabels -> "Name")
``````

Then, a subgraph of `g` defined by all the pathways from vertex 6 to 4 is:

``````fp = FindPath(g, 6, 4, Infinity, All)
hfp = HighlightGraph(g, Subgraph(g, fp, VertexLabels -> "Name"))
``````

I want to find the adjacency matrix of `hfp`, showing the highlighted edges in `hfp` in a 10 by 10 matrix (the size of the original digraph `g`).

## python – Problem in Bayesian Neural Networks PYMC3 code execution..error: (‘Variable type field must be a TensorType.’,)

I am trying to execute the following program and it is showing the following error: (‘Variable type field must be a TensorType.’, <Sparse(float64, csr)>, Sparse(float64, csr)).

I dont know why it is wrong.in the bold line( acts_1= pm.math.sigmoid(pm.math.dot(ann_input, weights_in_1)) )..can anyone help to solve this issue..thanks in advance…

program :

import theano.tensor as tt
import pymc3 as pm

X = x_vector.astype(floatX)
Y = y.astype(floatX)

X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size=.3)

ann_input = theano.shared(X_train.astype(‘float64’))
ann_output = theano.shared(Y_train.astype(‘float64’))

init_1 = np.random.randn(20, 6).astype(floatX)

with pm.Model() as nn_model:

``````mu_a = pm.Normal('mu_a', mu=0., sigma=100)
sigma_a = pm.HalfNormal('sigma_a', 100.)

weights_in_1 = pm.Normal('w_1', mu=mu_a, sd=sigma_a,
shape=(20, 6), testval=init_1)

***acts_1= pm.math.sigmoid(pm.math.dot(ann_input, weights_in_1))***

# Define likelihood
out = pm.Multinomial('likelihood', n=1, p=acts_1,
observed= ann_output)

step = pm.Metropolis()
trace = pm.sample(50000, step=step)
``````

## computer networks – Tearing down the FSM description of congestion control

I was going through the text Computer Networking- A Top-Down Approach by Kurose and Ross, there I found subtleties with the TCP congestion control FSM which is shown below:

Mainly I am having difficulty in understanding the action transmit new segment(s), as allowed and transition to the Fast Recovery state.

I have read the equivalent portions from the textbook Data Communications and Networking by Forouzan but there though the explanation is easy but there is no FSM or a programmatic approach.

Now let us consider the slow start phase as shown in the Kurose & Ross text:

The time diagram which they explain about the $$cwnd$$ doubling after each transmission round is easy and is just like what the Forouzan text says. But I find it difficult to understand the implementation based on the arc labeled with :

in the slow start phase.

1. Suppose the sender starts with $$cwnd = 1$$ $$MSS$$ then sends this (1st) segment to the network layer and awaits the acknowledgment.
2. The sender gets “new ACK” for the previous packet and increases $$cwnd$$ to $$2$$ $$MSS$$. Then in accordance to “transmit new segment(s), as allowed”, the sender sends $$2$$ segments (2nd and 3rd) to the network layer and awaits the acknowledgments.
3. Now the sender receives “new ACK” corresponding to 2nd segment and increases $$cwnd$$ to $$3$$ $$MSS$$. Then in accordance to “transmit new segment(s), as allowed”, the sender sends $$3$$ segments to the network layer and awaits the acknowledgments.
4. Now the sender receives “new ACK” corresponding to 3rd segment and increases $$cwnd$$ to $$4$$ $$MSS$$. Then in accordance to “transmit new segment(s), as allowed”, the sender sends $$4$$ segments to the network layer and awaits the acknowledgments.

From points 3 and 4, I find that the situation does not match with the slow start phase as shown in Fig 3.51. (i.e. the no. of segments sent are 1,2, 3,4 instead of 1,2,4)

I cannot understand the Fast recovery state’s action. Specifically the Forouzan text says :

Most TCP implementations have two reactions:

1. If a time-out occurs, there is a stronger possibility of congestion; a segment has probably been dropped in the network, and there is no news about the sent segments. In this case TCP reacts strongly:
a. It sets the value of the threshold to one-half of the current window size.
b. It sets cwnd to the size of one segment.
c. It starts the slow-start phase again.

2. If three ACKs are received, there is a weaker possibility of congestion; a segment may have been dropped, but some segments after that may have arrived safely since three ACKs are received. This is called fast transmission and fast recovery. In this case, TCP has a weaker reaction:
a. It sets the value of the threshold to one-half of the current window size.
b. It sets cwnd to the value of the threshold (some implementations add three segment sizes to the threshold).
c. It starts the congestion avoidance phase.

In the Forouzan text, there is no such transition to the Fast Recovery state. But here in Kurose there is such a state and there is an arc labeled :

whose working I do not quite understand in detail.

What extra work is the version in Kurose doing as compared to the one given in the Forouzan text? Can anyone explain me the subtleties with a comprehensive example covering all the cases of the FSM, so that I can understand the thing better.

## Why can’t we perform a replay attack on wifi networks

I was wondering that when a hacker is trying to hack a wifi network he would try to capture a handshake and then try to decrypt it,whereas when you wanna login to your wifi you would type in your password and the password would be encrypted then sent to the router which would decrypt it using a key.
So why can’t we just resend the encrypted password(the handshake) to the router without having to decrypt it like a replay attack.

## social networks – Instagram 429 Error during SEO Scanning

All pages (14000+, due to master layout) have a link to the Instagram brand page, and for some reason the SEO scanning tool is citing a 429 error for only one of the pages. I’m thinking it’s rate limiting the scanning bot, and wanted to see if adding a no-follow would solve that or not?