A graph is an abstract data structure. It holds nodes that are usually related to each other. A node is a dataset, typically in the form of ordered pairs. Nodes are either connected or not connected to another node. The relation between nodes is usually defined as an Edge. Graphs are useful for their ability to associate nodes with other nodes.
There are a few representations of Graphs in practice.
Leonhard Euler used to live in a town called "Königsberg." (Its name changed to Kaliningrad in 1946). The town is on the river Pregel. There is an island in the river. There are some bridges across the river. Euler wanted to walk around and use each of the bridges once. He asked if he could do this. In 1736, he published a scientific article where he showed that this was not possible. Today, this problem is known as the Seven Bridges of Königsberg. The article is seen as the first paper in the history of graph theory.
This article, as well as the one written by Vandermonde on the "knight problem," carried on with the "analysis situs" initiated by Leibniz. Euler's formula was about the number of edges, vertices, and faces of a convex polyhedron was studied and generalized by Cauchy and L'Huillier, and is at the origin of topology.
The fusion of the ideas coming from mathematics with those coming from chemistry is at the origin of a part of the standard terminology of graph theory. In particular, the term "graph" was introduced by Sylvester in an article published in 1878 in "Nature".
One of the most famous and productive problems of graph theory is the four color problem: "Is it true that any map drawn in the plane may have its regions colored with four colors, in such a way that any two regions having a common border have different colors?"
Graph theory is an important part of mathematics and computer science. To many such problems, exact solutions do exist. Many times however, they are very hard to calculate. Therefore, very often, approximations are used. There are two kinds of such approximations, Monte-Carlo algorithms and Las-Vegas algorithms.
Goatee
A goatee is a beard formed by a tuft of hair under the chin, resembling that of a billy goat.
Herm
Herm is the smallest of the Channel Islands that is open to the public.
Herm is only 1½ miles long. Cars are banned from the small island just like its Channel Island neighbour, Sark. Unlike Sark, bicycles are banned too. The sandy white beaches make Herm a walker's paradise.
Population: 60 (2002).
History
History is the study of past events. People know what happened in the past by looking at things "from" the past including sources (like books, newspapers, and letters) and artifacts (like pottery, tools, and human or animal remains.) Libraries, archives, and museums collect and keep these things for people to study history. A person who studies history is called a historian. A person who studies pre-history and history through things left behind by ancient cultures is called an archaeologist. A person who studies mankind and society is called an anthropologist. The study of the sources and methods "used to study and write" history is called historiography.
People can learn about the past by talking to people who remember things that happened at some point in the past. This is called oral history. For example, when people who had been slaves and American Civil War survivors got old, some historians recorded them talking about their lives, so that history would not be lost.
In old times people in different parts of the world kept separate histories because they did not meet each other very often. Some groups of people never met each other. The rulers of Medieval Europe, Ancient Rome and Ancient China each thought that they ruled the only important parts of the world and that other parts were "barbarian". But they were still connected, even if they didn't realize it.
Current events, modern economic history, modern social history and modern intellectual history take very different views of the way history has affected the way that we think today.
Health
Health is "a state of complete physical, mental, and social well-being and not merely the absence of disease" according to the World Health Organization (WHO). "Physical" is about the body. "Mental" is about how people think and feel. "Social" talks about how people live with other people. It is about family, work, school, and friends.
Physical fitness refers to good body health. It is dependent on genetic determinators and also on social, economic and ecological factors. That means, one's genes are partly responsible for one's physical health, but also other circumstances: where you live, how clean or polluted your water and the air around you is and also how good your social and medical system is. It is also the result of regular exercise, proper diet and nutrition, and proper rest for physical recovery. A person who is physically fit will be able to walk or run without getting breathless and they will be able to carry out the activities of everyday living and not need help. How much each person can do will depend on their age and whether they are a man or woman. A physically fit person usually has a normal weight for their height. The relation between their height and weight is called their Body Mass Index. A taller person can be heavier and still be fit. If a person is too heavy or too thin for their height it may affect their health. Better health is central to human happiness and well-being. It also makes an important contribution to economic progress, as healthy populations live longer, are more productive, and save more. Many factors influence health status and a country's ability to provide quality health services for its people.
Mental health refers to a person's emotional and psychological well-being. "A state of emotional and psychological well-being in which an individual is able to use his or her thinking and emotional (feeling) abilities, function in society, and meet the ordinary demands of everyday life."
One way to think about mental health is by looking at how well a person functions. Feeling capable and efficient; being able to handle normal levels of stress, have good friends and family, and lead an independent life; and being able to "bounce back," or recover from hardships, are all signs of mental health.It’s normal for all of us to feel worried, sad, upset, or have difficult emotions from time-to-time. For most people though, these feelings are only temporary and are resolved without causing any long-term problems. However, for some people, these negative feelings can become worse over time and lead to a mental health problem such as depression, anxiety, stress or obsessive-compulsive disorder (OCD).
Public health refers to trying to stop a disease that is unhealthy to the community, and does not help in long life or promote your health. This is fixed by organized efforts and choices of society, public and private clubs, communities and individuals.
It is about the health of many people, or everybody, rather than one person. Public health stops instead of encouraging a disease through surveillance of cases. To prevent being sick, it is good to act according to some simple advice: Hand washing, regular check-ups, vaccination programmes, drinking clean water and using condoms. When infectious diseases break out, washing hands for about 30 seconds may be especially important. Sometimes it is necessary to avoid masses of people or wear a surgical mask to protect yourself and to stop the spreading of the disease. Teaching people how to live healthily and educate them, especially about sex and child-birth, is also very important.
Harbor