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9

Fewer nodes/edges (or edges with fixed weights) means that there are fewer parameters whose values need to be found, and this typically reduces the time to learn. Also, when there are fewer parameters, the space that can be expressed by the neural network has fewer dimensions, so the neural network can only express more general models. It is thus is less ...

6

The original division and allocation of IP addresses used a system called classful IP addressing. This is the division to which you are referring, in which a class A network would receive all addresses X.0.0.0-X.255.255.255 and have over 16.5 million host addresses. As designated below, the network bits in classful addressing are divided in 8-bit groupings. ...

5

By pruning edges you've reduced the search space for the training algorithm, which will have an immediate payoff in time performance. You've also introduced constraints on the functions the network can model. The constraints may force your model to find a more general solution since the more accurate one is unreachable. A common technique for training neural ...

3

Wasting ports to achieve an exact number of terminals is a common attribute of staged networks (butterfly, benes, folded-clos, etc.). The mesh, torus, and flattened butterfly topologies are a bit better because each dimension can have a different width, but this results in having uneven bisection bandwidth along each dimensional cut. The HyperX topology is a ...

3

You want to solve the problem of graph isomorphism (GI). GI is not known to be in P or NP-complete; that is, we do not know any efficient algorithms. Many algorithms have been proposed for GI. None applies to all graphs and is always fast, but you may be able to find one that is sufficiently fast in your application. In 2015, Babai proposed a quasi-...

3

Not really a straight answer, but I don't have the ability to comment yet. I think you are confusing the Koch snowflake with the Sierpinski gasket/triangle. A Koch topology would just be equivalent to a path. The Sierpinski triangle has the properties you describe. A quick google shows a wealth of papers and webpages on Sierpinski networks, although there ...

2

There are a couple of test sets mentioned in Stochastic blockmodels and community structure in networks by Karrer and Newman. One of them is the Karate Club Network, which is rather small, and the other is the Political Blog Network which is bigger. As far as I know, there is no gold-standard for testing clustering algorithms.

2

I think it's unlikely you're going to get good results. Neural networks typically require a large training set. With only a few dozen or so examples, I doubt you'll have a large enough training set for this to work well. So, what could possibly go wrong? I suspect the most likely outcome is that you'll get useless results. That said, if you really ...

2

This paper [1] presents a method to construct arbitrarily sized benes networks using a recursive approach. Arbitrary Size Benes Networks by Chihming Chang and Rami Melhem in Parallel Processing Letters, Volume 7, 1997

1

Certainly it is possible. For example, in the following study the Indian railway network was analyzed. Small-world properties of the Indian railway network. Parongama Sen, Subinay Dasgupta, Arnab Chatterjee, P. A. Sreeram, G. Mukherjee, and S. S. Manna. Phys. Rev. E 67, 036106 – 2003 In another study, the Chinese railway network was considered. W. Li, ...

1

One would say that P2P is better. But in reality, you cannot tell by the information you provided. For instance, the bandwidth depends on queuing delays. Therefore, assume that one of the nodes in the P2P network has a very small queue (or overloaded), while our server is super powerful and its queue is hugly big ! Similarly, it depends on the latency of ...

1

Here is how some other blockchain protocols ensure consensus about the next block: Ethereum currently uses a Proof-of-Work approach that is similar to Bitcoins, but will change the protocol to use a Proof-of-Stake mechanism instead. This means that people who have a lot of ETH (the Ethereum currency) or have had ETH for a long time and haven't written a ...

1

Here's how Bitcoin works. I suppose we could say that each node can "propose" a different next block. What this really means is that each node can select a "proposed" next block and start mining to attempt to append that block to the blockchain. Bitcoin's proof-of-work basically creates a lottery among all of the nodes who are doing this; it's random ...

1

To prove that the diameter of the undirected ring topology is $n/2$: Find two vertices $x,y$ at distance $n/2$. Show that any two vertices $x,y$ are at distance at most $n/2$. By the way, the diameter is more accurately $\lfloor n/2 \rfloor$.

1

You need to differentiate between centralization/decentralization on the one hand and distributed/non-distributed on the other hand. Centralization Centralization tells you where the processing gets done. Fully centralized systems do all their processing in one place. Distribution Distribution has nothing to do with processing. It just relates to ...

1

Bigger frames mean a higher useful data fraction (same header size, more payload). But bigger frames mean a higher probability of the frame getting corrupted by random errors (thus getting lost). Larger frames mean higher latencies (need to wait for all of it to arrive, be checked, and handed to the application to be able to use any data in it). They also ...

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