Some random posts on twitter rekindled my fascination with ML. Chris Olah has an amazing explanation on the beauty in ML. Got to learn that even group theory is applied to ML. Link
The narrator began by explaining the origins of a problem that involves uniting two branches of mathematics: algebra and harmonic analysis. The first person to consider this connection was the mathematician Srinivasa Ramanujan, who made a conjecture that an infinite series in algebraic terms could be expressed in modular form, which is a symmetrical structure in harmonic analysis.
Many years later, Andrew Wiles used this principle to prove Fermat’s Last Theorem by contradiction. He discovered that all elliptic curves could be described as infinite series, and that these curves also have a modular form. This led to the popular conjecture that all infinite series have a modular form, which would mean that an elliptic curve must also be modular. However, this conjecture was later disproved by the existence of the Frey elliptic curve, which is not modular. This result directly implies that there is no solution to Fermat’s Last Theorem.
Kerberos is an auth method where trust is put on a Key distribution center(KDC). Here are the steps:
Server A wants to securely talk to Server B on the same network but it doesn’t know how. Server A tells the KDC’s Server to let it talk to the ticket granting system(TGS) which is part of KDC.
A sends some info about itself, a random number to KDC. KDC finds if it’s an authenticated user and sends {Kat, Time to Live, same random number} all encrypted with Kas(public key of Server A and Server S. Also to notify TGS of this it sends other packet with {Kat, some info on A, TTL} encrypted with Kst. Thus TGS knows that this has arrived directly from the Server of the key.
Server A sends some info on B, TTL to which TGS send {Kab, TTL, some random number} encrypted with Kat alonwith { Kab, TTL, some info on A} encrypted with Kbt so server B knows that server is legit and have authenticated with KDC first. Thus
Dark Matter is not so fascinating, I have known about it for quite some time now but I was unaware of the working of experiments. So here is my exploration of it with Derek:
DAMA-LIBRA found a strange oscillating curve for the amount of concentration of DM around our galaxy. The reason that they hypothesized is that DM is not spread uniformly around our galaxy but rather it is divided rather in unequal proportion thus causing it to be dense for some time while sparse for some other.
To prove this hypothesis DAMA-LIBRA teamed up with an observatory in Australia because seasons are polar opposites so their curve would be slightly different/opposite. The rest of the video describes the experiment in Australia.
They used 7 cylinders each containing 1 Kg of pure NaI which when hit by WIMPs(candidate particle for DM) emits a photon which causes scintillation which are detected by photodetectors. Pure NaI contains radioactive Potassium which decays into electron and gamma rays which also produce scintillation so they are submerged in a liquid that just detected gamma particles. Thus if some detectors fire simultaneously then it was decay of radioactive Potassium. Cosmic rays which consist of muons might also disturb the experiment thus a Cosmic ray detector is placed at the top of the container. As the experiment is run underground there might be traces of radiation thus walls are painted to absorb it. Finally the whole chamber is surrounded by 120 tons of steel and plastic. It would take about a decade before the results show up.
Benford’s law states that in any real-world dataset consisting of data in orders of magnitude, the number 1 will appear as the most significant digit about 33.1% of the time, followed by the number 2 and then the number 3. This results in an exponential decay of the occurrence of natural numbers as the most significant digit. Benford’s law is typically applied to data that is in orders of magnitude and may not hold for datasets with a uniform or normal distribution. However, it has a wide range of applications, including detecting financial fraud, analyzing electricity bills, estimating the size of rivers, and even analyzing COVID-19 case data reported by different states.
For example, during the 2020 presidential election, there was speculation that Joe Biden’s voting data did not follow Benford’s law. However, this was later disproved as the analysis only considered the first digit of the data and ignored the fact that the population distribution in Chicago was normal, meaning that it would not be expected to follow Benford’s law. Similarly, a YouTube channel called Stand Up Maths demonstrated that when the last digit of Donald Trump’s voting data was analyzed, there was a significant error, leading to suspicions of fraud. However, these claims remain unproven.
Benford’s law has also been featured in popular media, such as the television show “Ozark.” For more information on Benford’s law, Wikipedia is a good resource. Additionally, any series that follows a power law or is expanded geometrically will also strongly follow Benford’s law, such as the Fibonacci series.
]]>Wi-Fi is a type of radio wave signal that is used to transmit and receive data. In order to establish a connection, Wi-Fi routers constantly send out beacon packets at certain frequencies, which consumes power even when the router is not in use. To reduce power consumption and increase the range of the signal, beacon packets are typically sent out over a period of time, allowing them to effectively reach large distances. When you view the Wi-Fi signal settings on your device, you are seeing a list of all the beacon packets that your device has received.
It is interesting to note that two routers cannot transmit packets at the same frequency at the same time, as this can cause destructive interference. To prevent this, routers have a “listen first, then transmit” policy, in which they check if any nearby routers are transmitting on the same frequency before transmitting themselves. This can affect the speed of both routers.
Most Wi-Fi routers in 2022 operate on the 2.4 GHz band, which is made up of several channels, or sub-frequency ranges, over which the router can choose to transmit its data. When there are many Wi-Fi devices in the area, the chances of a frequency match increase, which can reduce the speed of all the devices. Dual-band routers, which became available with Wi-Fi 5, can transmit on both the 2.4 GHz and 5 GHz bands, which can help to reduce interference. The latest version of Wi-Fi, called Wi-Fi 6 (802.11ax), has even higher efficiency and faster theoretical download speeds. It also enables a technology called Multi-User Multi-Input-Multi-Output (MU-MIMO), which allows multiple users to connect to the router simultaneously and allows the router to transmit beacon packets at multiple frequencies.
An interesting fact is that a slow Wi-Fi signal that is far away can affect your connection more harshly than a fast Wi-Fi signal that is close by. This is because the signal has to travel further, which can result in more interference and a weaker connection. According to a Cisco paper on best practices for Wi-Fi in an office setting, it is recommended to use a combination of the 5 GHz band (which is less crowded) and the 2.4 GHz band (which is more crowded) to maximize the speed and reliability of the Wi-Fi connection.
]]>Read a CloudFlare blog about the recent internet outage in Kherson, Ukraine. Apparently Russian had replaced the Ukrainian ISP and connected for some time to the Russian internet network thus they were able to monitor it entirely. CloudFlare showed a graph in which they depicted a spike in their Moscow Data Center.
Difference between Simple Strategy and Network Topology Strategy is more conspicuous. Simple Strategy will choose the next irrespective of its DC/RACK location, on the other hand NTS will be aware of the Network Topology(through our chosen snitch) and will group based on DC/Rack. Performance is same for SS and NTS in our case.
NTS power is revealed when we put suffixes(cassandra-rackdc.properties) to form virtual groups for asymmetrical replication groups i.e some servers could be used for HA data and some other tasks where latency is acceptable we can query it from other nodes.
Learned about consistency levels and still could not find the reason behind last week’s error. When hinted handoff is turned on, the coordinator stores data of replica nodes that are not responding for 3hrs after which it flushes it.
Cassandra read path is more complex than write path. Anyone can be a coordinator node in a cluster. More num tokens has an inverse effect on the fault tolerance of the cluster.
Learned about the science of butterfly effect(Chaos). It all started few years after Principia was released, when someone challenged Newton to find a solution to the three-body problem. Poincare termed it chaos. It was picked up again when a meteorologist whose name I forgot was trying to predict the state of the atmosphere based on some 12 variables(temp, pressure..). When he was redoing his calculations rather than doing it from start he took half observations from last calculation and found the data was completely divergent. This started the chaos theory, small irrelevant change and a huge impact down the lane. Swinging of a double pendulum is chaotic, its phase-angle plot reveals a butterfly like shape hence the name. They are also linked to FRACTALS.
]]>Learned about Schema building, Start Apollo server, filling mocks, use studio for local development, manual query, manual type, learned about gql on server side, learned about query resolvers, apollo client cache, wrote a resolver, learned about resolver arguments, anatomy of a graphql request
Made an axios request, learned some important options which might be useful like with credentials and basic auth. Want to explore proxy and content length limitation, valid status function might be useful for initial MVP.
What they are? Build over HTTP, diff between http 1 and 1.1, switching protocol code, websocket uses and building a demo app. WS is http underneath, Built a demo app, ws connection between localhost and chrome- works like realtime chat.
Multithreading: its meaning and walkthrough, if not implemented correctly than how its a waste, how to prevent such scenarios like an interesting approach was to prevent other threads from executing and overriding the common register. THey used mutexes to perform this kind of event locking.
Learned that VPN is apparently over UDP not TCP. Sounds strange but havent known the reason yet.