Mathematics Survey

On many networks you’ll find lots of little packets of data flying all over the place.  These small packets are commonly known as tinygrams and on most standard Local area networks they are not really an issue.  This is basically because your average local network is not really congested and this data doesn’t cause much of an issue.  However when you are using a slower Wide Area Network (WAN) then they become a very big problem.  RFC was released containing an elegant solution to this problem and it’s called Nagle’s algorithm.

This algorithm states that when a TCP connection is still waiting for an acknowledgement, then no small segments can be sent until the ack is received.  Instead then small parcels of data are collected by TCP and sent in a single segment when the acknowledgement is received.   The real advantage of this algorithm is that it is self clocking.  The faster the ACKs are received then the quicker the data is sent out.  This can help greatly on a slower WAN as it will significantly reduce the number of these tinygrams which are sent across the network.

It has been so successful that it is currently enabled on all Microsoft Operating systems.  However some gamers insist that it can affect performance. Of course when that single delay on a click, command can deal your character a premature death – this stuff is important. Although if you’re playing a game based across the Atlantic then you may be better advised to invest in a US IP address  instead and not mess around with your registry.  It’s the safest option if you can afford it and you can find more information on this page – http://www.proxyusa.com/usvpn

If you do want to turn it off them you’ll need to modify the following registry key –

HKEY_LOCAL_MACHINE\\SYSTEM\\CurrentControlSet\\Services\\Tcpip\\Parameters\\Interfaces

Under here you’ll see your network interfaces listed. Pick the one which you want to modify (i.e. your internet facing card) and then you need to create a couple of new entries. You need two new Dwords – first one called TcpAckFrequency and the second one TCPNoDelay (both case sensitive). Then set the values of both these settings to Value Data = 1, that’s all their is to it. You can then reboot your machine and the Nagle Algorithm settings will not apply to that interface.

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In essence a social network is made up by an number of points all connected to each other by a specific relationship.  They could be members of a certain group, be ’friends’ or have sent someone a message or ’like’.  The units don’t have to be just people though, they can be places, groups, companies or even photos or articles.

The main issues with social networks can be quite easy to define but when you try and assess them things get a little more confusing.  For a company like Facebook understanding these relationships is core to their ideal of bringing people together (and making money out of them!).  Trying to work out which individuals can be connected is a key aim and to understand it you  have to ask some basic questions.

• Who is connected to who else?
• How Can you Connect Sub Groups of People
• Are Some Groups of People better connected than others.

It can be summaried into defining communities and understanding their relationships.  So how can we use maths to understand and help answer these questions?  Well the easiest way is to graph the various networks – this can be achieved by partitioning a social network into specific groups and sub networks,.

The subject can become quite complicated but if you’re interested in a good starting point try Moses Boudourides, search online for “An Introduction to Community Detection in Graphs”

He helps explain some excellent techniques and approaches to help breakdown the networks into more manageable subsets. This helps the overall analysis of the different nodes and their relationships between each other.  For a primer into the SEO science of social networking then this article comes recommended – How to Use Social Networking in SEO.  Although the analysis of social networks may seem quite confusing at first, in reality they offer a fascinating way to study relationships and social groups interacting with each other.

Henry Haversham

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When you find the best wine club available, it’s a good bet that you’re joining along with a few thousand other people.  Honestly, that makes sense on a number of levels since it is natural to want the best of anything that you’re involved with right?

Anyway, the math for a wine club seems simple right?  I mean, money comes in, they buy wine and money goes out.  It’s not quite that simple though.  If we’re talking about accounting then there are some choices which the average club needs to make.  Mainly, what type of accounting systems are they going to use?

Straight line cash in and cash out accounting like a big business?  Or more complex, but appropiate, cost of goods sold? Cost of goods sold accounting takes into account the price that the wine club paid for each bottle of wine which was sold and  assumes that the club has enough money in the bank to pay for sufficient inventory levels.

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It was back in 1998 that Brin and Page, two young PhD students studying at the computer department in Stanford created the world’s first algorithm for ranking web pages.  The method has since become known as PageRank and was the start of a hugely successful company you might have heard of called Google.  Their company became an almost overnight success, the students took a leave of absence from Stanford whilst they turned themselves into Billionaires.

So what is PageRank and what does it mean.  The fundamental idea is that every link pointing to a web site is a recommendation as to it’s value.  Basically the more links the more valuable the resource and the more likely to provide information to help the searcher.  Up to this point all the search engines had tried to rank web sites based on what was on  the page.

The problem with this method is that it was very easy to manipulate and often ranked poor quality pages which slotted into the algorithm well.  Using external sources and recommendations was truly a major improvement in the quality of web sites that were selected to appear in Google’s results.

The algorithm behind PageRank is a mathematically elegant and spohisticated solution to a specific problem. In a perfect world these links are votes from the global internet community, only pages that justify these links would have the quality to appear in the search results.

There is an important assumption with this algorithm and one that forms the basic of many of the articles on this Technical site – http://www.changeipaddress.net/british-ip-address/ – that is the random surfer.  It’s one of the assumptions behind PageRank – a person randomly arriving at a web page and clicking on that link is voting in some respects for that site.  The algorithm was quite simplistic then but is developing rapidly.  Now the amount of time a user spend on a site is important, also the less presses of the ’back button’ the better.

Basically the more engaging, useful and interesting a site is the more sueful the site is deemed to be.  Google continues to dominate the ’Search market’ using this technology.

James Bellings

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Recreational mathematics might seem as a term related to financial or tourism industry, however it is one of so called umbrella terms, referred to mathematical games such as puzzles, mathematical logic games, juggling, origami and others. This part of mathematics is often required deductive reasoning, aesthetics of higher maths and even amusing stories from the history of mathematics or mathematicians themselves.

First publications about recreational mathematics dates back to 1939 from a group of scientists in Cambridge University. Since than, the theory has developed drastically and many famous scientists such as Stephen Hawking, Martin Gardner and Roger Penrose, have been studying and developing the theory. More than 60 scientific articles has been published regarding recreational maths and nowadays it involves such things as magical numbers, numerology, folding, sports, dissection and even mathematical humor.

Mathematical games are most likely played by several players and involves an extensive knowledge of mathematics applied for real life situations, mathematical logic and common sense. Mathematical game rules goes strictly together with mathematical theory and is a great way to check your high-school knowledge as well as more in-depth problems resolved by higher maths. Such simple games can be played with friends or family and are truly educational and fun. It is perfect for a family holiday as well as break out of the city. Mathematical games can develop your logic and the way of thinking as well as taking your mind of work and every day troubles.

Recreational mathematics can be truly beneficial for you, your family and friends, especially as an nice escape from city to a quiet rented luxury lodge near lake for example. You can discover some really great luxury holiday deals in Ireland from anywhere in the world, just route your connection through an Irish proxy and you’ll be able to book online:  Remember to revise your mathematical skills and even show off with your recreational mathematics knowledge while resolving mathematical game problems in style!

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