The Hayflick limit (or Hayflick phenomenon) is a phenomenon of cell division in tissue culture. It is the number of times a normal human cell population divides until cell division stops.
We now know that the telomeres on each cell's chromosomes get slightly shorter with each new cell division, until they reach a critical length.
The idea of the Hayflick limit was suggested by American anatomist Leonard Hayflick in 1961, at the Wistar Institute in Philadelphia, Pennsylvania. Hayflick showed that a population of normal human fetal cells in a cell culture will divide between 40 to 60 times. The population then goes into senescence. This refutes the idea of Nobel laureate Alexis Carrel that normal cells are potentially immortal.
Each mitosis slightly shortens each of the telomeres on the chromosomes of the cells. Telomere shortening eventually makes cell division impossible, and this ageing of the cell population may cause the overall physical ageing of the human body.
The process of telomere shortening leads to apoptosis, the technical name given to programmed cell death. Although the Hayflick experiments were done on human cells in tissue culture, there is nothing special about human cells which would not be found in the cells of other living organisms. Apoptosis is thought to happen in all multicellular organisms. The 2002 Nobel Prize in Medicine was awarded to Sydney Brenner, H. Robert Horvitz and John E. Sulston for their work identifying genes that control apoptosis. The genes were found by studies in the nematode "Caenorhabditis elegans". These same genes function in humans for apoptosis.
Cantor's diagonal argument
Cantor's diagonal argument is a mathematical method to prove that two infinite sets have the same cardinality. Cantor published articles on it in 1877, 1891 and 1899. His first proof of the diagonal argument was published in 1890 in the journal of the German Mathematical Society (Deutsche Mathematiker-Vereinigung). According to Cantor, two sets have the same cardinality, "if it is possible to associate an element from the second set to each element of the first set, and to associate an element of the first set to each element of the second set". This statement works well for sets with a finite number of elements. It is less intuitive for sets with an infinite number of elements.
The example below uses two of the simplest infinite sets, that of natural numbers, and that of positive fractions. The idea is to show that both of these sets, formula_1 and formula_2 have the same cardinality.
First, the fractions are aligned in an array, as follows:
Next, the numbers are counted, as shown. Fractions which can be simplified are left out:
That way, the fractions are counted:
By omitting fractions that can still be simplified, there is a bijection which associates each element of the natural numbers, to one element of the fractions:
To show that all natural numbers and the fractions have the same cardinality, the element 0 needs to be added; after each fraction its negative is added;
That way, there is a complete bijection, which associates a fraction to each natural number. In other words: both sets have the same cardinality. Today, sets that have the same number of elements than the set of natural numbers are called countable. Sets which have fewer elements than the natural numbers are called at most countable. With that definition, the set of rational numbers / fractions is countable.
Infinite sets often have properties which go against intuition: David Hilbert showed this in an experiment which is called Hilbert's paradox of the Grand Hotel.
The set of real numbers does not have the same cardinality than those of the natural numbers; there are more real numbers than natural numbers. The idea outlined above influenced his proof. In his 1891 article, Cantor considered the set "T" of all infinite sequences of binary digits (i.e. each digit is zero or one).
He begins with a constructive proof of the following theorem:
To prove this, given an enumeration of elements from "T", like e.g.
The sequence "s" is constructed by choosing the 1st digit as complementary to the 1st digit of "s" (swapping 0s for 1s and vice versa), the 2nd digit as complementary to the 2nd digit of "s", the 3rd digit as complementary to the 3rd digit of "s", and generally for every "n", the "n" digit as complementary to the "n" digit of "s". In the example, this yields:
By construction, "s" differs from each "s", since their "n" digits differ (highlighted in the example).
Hence, "s" cannot occur in the enumeration.
Based on this theorem, Cantor then uses a proof by contradiction to show that:
He assumes for contradiction that "T" was countable. In that case, all its elements could be written as an enumeration "s", "s", … , "s", … .
Applying the previous theorem to this enumeration would produce a sequence "s" not belonging to the enumeration.
However, "s" was an element of "T" and should therefore be in the enumeration.
This contradicts the original assumption, so "T" must be uncountable.
Arrondissements of the Deux-Sèvres department
There are 3 arrondissements in the Deux-Sèvres department. The French departments, and in other countries, are divided into "arrondissements", which may be translated into English as districts (in some cases, as boroughs).  The capital of an arrondissement is called a subprefecture.
If the prefecture (capital) of the department is in an arrondissement, that prefecture is the capital of the arrondissement, acting both as a prefecture and as a subprefecture.
Arrondissements are further divided into communes.
The arrondissements of Deux-Sèvres are:
Since its creation, the Deux-Sèvres department has had some changes:
Arrondissement of Bressuire
The arrondissement of Bressuire is an arrondissement of France, in the Deux-Sèvres department, Nouvelle-Aquitaine region. Its capital is the city of Bressuire.
When the Deux-Sèvres department was created on 1790, Bressuire was not one of the original districts but, in 1804, it was made one of the "arrondissements" of the department when the subprefecture of Thouars was moved to Bressuire.
Bressuire is the northernmost "arrondissement" of the department. It is bordered to the north by the Maine-et-Loire department, to the east by the Vienne department, to the south by the "arrondissement" of Parthenay and to the west by the Vendée department.
It has an area of , and a population of 96,703 inhabitants for a density of inhabitants/km².
After the reorganisation of the cantons in France, cantons are not subdivisions of the "arrondissements" so they could have "communes" that belong to different "arrondissements".
In the "arrondissement" of Bressuire, there are 3 cantons with all their "communes"  in the "arrondissement": Bressuire, Mauléon and Thouars,
The following table shows the distribution of the "communes" in the "arrondissement" of  Bressuire:
The "arrondissement" of Bressuire has 53 "communes"; they are (with their INSEE codes)ː
Cynthia Kenyon
Cynthia Jane Kenyon (born February 21, 1954) is an American molecular biologist and geneticist. She does research on the genetics of aging in the model organism "Caenorhabditis elegans", which is a roundworm.
Kenyon did postdoctoral studies with Nobel laureate Sydney Brenner at the MRC Laboratory of Molecular Biology in Cambridge, England, studying the development of "C. elegans".
Since 1986 she has been at the University of California, San Francisco (UCSF), as the Herbert Boyer Distinguished Professor of Biochemistry and Biophysics, and now as an American Cancer Society professor. She is also Vice President of Aging Research at Calico, a new company focused on health, well-being, and longevity.
Her early work led to the discovery that hox genes, known to pattern the body segments of the fruit fly "Drosophila", also pattern the body of "C. elegans". These findings showed that hox genes were part of an ancient and fundamental metazoan patterning system.