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Kirchhoff's theorem

In the mathematical field of graph theory, Kirchhoff's theorem or Kirchhoff's matrix tree theorem named after Gustav Kirchhoff is a theorem about the number of spanning trees in a graph, showing that this number can be computed in polynomial time from the determinant of a submatrix of the Laplacian matrix of the graph; specifically, the number is equal to any cofactor of the Laplacian matrix. Kirchhoff's theorem is a generalization of Cayley's formula which provides the number of spanning trees in a complete graph.

Kirchhoff's theorem relies on the notion of the Laplacian matrix of a graph, which is equal to the difference between the graph's degree matrix (a diagonal matrix with vertex degrees on the diagonals) and its adjacency matrix (a (0,1)-matrix with 1's at places corresponding to entries where the vertices are adjacent and 0's otherwise).

For a given connected graph G with n labeled vertices, let λ1, λ2, ..., λn−1 be the non-zero eigenvalues of its Laplacian matrix. Then the number of spanning trees of G is

 * $$t(G)=\frac{1}{n} \lambda_1\lambda_2\cdots\lambda_{n-1}\,.$$

An English translation of Kirchhoff's original 1847 paper was made by J. B. O'Toole and published in 1958.

An example using the matrix-tree theorem

First, construct the Laplacian matrix Q for the example diamond graph G (see image on the right):

 * $$Q = \left[\begin{array}{rrrr}

2 & -1 & -1 & 0 \\ -1 & 3 & -1 & -1 \\ -1 & -1 & 3 & -1 \\ 0 & -1 & -1 & 2 \end{array}\right].$$

Next, construct a matrix Q* by deleting any row and any column from Q. For example, deleting row 1 and column 1 yields

 * $$Q^\ast =

\left[\begin{array}{rrr} 3 & -1 & -1 \\ -1 & 3 & -1 \\ -1 & -1 & 2 \end{array}\right].$$

Finally, take the determinant of Q* to obtain t(G), which is 8 for the diamond graph. (Notice t(G) is the (1,1)-cofactor of Q in this example.)

Proof outline
(The proof below is based on the Cauchy–Binet formula. An elementary induction argument for Kirchhoff's theorem can be found on page 654 of Moore (2011). )

First notice that the Laplacian matrix has the property that the sum of its entries across any row and any column is 0. Thus we can transform any minor into any other minor by adding rows and columns, switching them, and multiplying a row or a column by −1. Thus the cofactors are the same up to sign, and it can be verified that, in fact, they have the same sign.

We proceed to show that the determinant of the minor M11 counts the number of spanning trees. Let n be the number of vertices of the graph, and m the number of its edges. The incidence matrix E is an n-by-m matrix, which may be defined as follows: suppose that (i, j) is the kth edge of the graph, and that i < j. Then Eik = 1, Ejk = −1, and all other entries in column k are 0 (see oriented incidence matrix for understanding this modified incidence matrix E). For the preceding example (with n = 4 and m = 5):

E = \begin{bmatrix} 1 & 1 &  0 &  0 &  0 \\  -1 &  0 &  1 &  1 &  0 \\   0 & -1 & -1 &  0 &  1 \\   0 &  0 &  0 & -1 & -1 \\ \end{bmatrix}. $$

Recall that the Laplacian L can be factored into the product of the incidence matrix and its transpose, i.e., L = EET. Furthermore, let F be the matrix E with its first row deleted, so that FFT = M11.

Now the Cauchy–Binet formula allows us to write

 * $$\det\left(M_{11}\right) = \sum_S \det\left(F_S\right)\det\left(F_S^{\mathrm{T}}\right) = \sum_S \det\left(F_S\right)^2$$

where S ranges across subsets of [m] of size n − 1, and FS denotes the (n − 1)-by-(n − 1) matrix whose columns are those of F with index in S. Then every S specifies n − 1 edges of the original graph, and it can be shown that those edges induce a spanning tree if and only if the determinant of FS is +1 or −1, and that they do not induce a spanning tree if and only if the determinant is 0. This completes the proof.

Cayley's formula
Cayley's formula follows from Kirchhoff's theorem as a special case, since every vector with 1 in one place, −1 in another place, and 0 elsewhere is an eigenvector of the Laplacian matrix of the complete graph, with the corresponding eigenvalue being n. These vectors together span a space of dimension n − 1, so there are no other non-zero eigenvalues.

Alternatively, note that as Cayley's formula counts the number of distinct labeled trees of a complete graph Kn we need to compute any cofactor of the Laplacian matrix of Kn. The Laplacian matrix in this case is

\begin{bmatrix} n-1 & -1     & \cdots & -1      \\ -1 & n-1     & \cdots & -1      \\ \vdots & \vdots& \ddots & \vdots \\ -1 & -1     & \cdots & n-1      \\ \end{bmatrix}. $$

Any cofactor of the above matrix is nn−2, which is Cayley's formula.

Kirchhoff's theorem for multigraphs
Kirchhoff's theorem holds for multigraphs as well; the matrix Q is modified as follows: Cayley's formula for a complete multigraph is mn-1(nn-1-(n-1)nn-2) by same methods produced above, since a simple graph is a multigraph with m = 1.
 * The entry qi,j equals −m, where m is the number of edges between i and j;
 * when counting the degree of a vertex, all loops are excluded.

Explicit enumeration of spanning trees
Kirchhoff's theorem can be strengthened by altering the definition of the Laplacian matrix. Rather than merely counting edges emanating from each vertex or connecting a pair of vertices, label each edge with an indeterminate and let the (i, j)-th entry of the modified Laplacian matrix be the sum over the indeterminates corresponding to edges between the i-th and j-th vertices when i does not equal j, and the negative sum over all indeterminates corresponding to edges emanating from the i-th vertex when i equals j.

The determinant of the modified Laplacian matrix by deleting any row and column (similar to finding the number of spanning trees from the original Laplacian matrix), above is then a homogeneous polynomial (the Kirchhoff polynomial) in the indeterminates corresponding to the edges of the graph. After collecting terms and performing all possible cancellations, each monomial in the resulting expression represents a spanning tree consisting of the edges corresponding to the indeterminates appearing in that monomial. In this way, one can obtain explicit enumeration of all the spanning trees of the graph simply by computing the determinant.

For a proof of this version of the theorem see Bollobás (1998).

Matroids
The spanning trees of a graph form the bases of a graphic matroid, so Kirchhoff's theorem provides a formula to count the number of bases in a graphic matroid. The same method may also be used to count the number of bases in regular matroids, a generalization of the graphic matroids.

Kirchhoff's theorem for directed multigraphs
Kirchhoff's theorem can be modified to count the number of oriented spanning trees in directed multigraphs. The matrix Q is constructed as follows: The number of oriented spanning trees rooted at a vertex i is the determinant of the matrix gotten by removing the ith row and column of Q
 * The entry qi,j for distinct i and j equals −m, where m is the number of edges from i to j;
 * The entry qi,i equals the indegree of i minus the number of loops at i.

Counting spanning k-component forests
Kirchhoff's theorem can be generalized to count $k$-component spanning forests in an unweighted graph. A $k$-component spanning forest is a subgraph with $k$ connected components that contains all vertices and is cycle-free, i.e., there is at most one path between each pair of vertices. Given such a forest F with connected components $F_1, \dots, F_k$, define its weight $w(F) = |V(F_1)| \cdot \dots \cdot |V(F_k)|$ to be the product of the number of vertices in each component. Then

\sum_F w(F) = q_k, $$

where the sum is over all $k$-component spanning forests and $q_k$ is the coefficient of $x^k$  of the polynomial

(x+\lambda_1) \dots (x+\lambda_{n-1}) x. $$ The last factor in the polynomial is due to the zero eigenvalue $\lambda_n=0$. More explicitly, the number $q_k$ can be computed as

q_k = \sum_{\{i_1, \dots, i_{n-k}\}\subset\{1\dots n-1\}} \lambda_{i_1} \dots \lambda_{i_{n-k}}. $$ where the sum is over all n–k-element subsets of $\{1, \dots, n\}$. For example

$$\begin{align} q_{n-1} &= \lambda_1 + \dots + \lambda_{n-1} = \mathrm{tr} Q = 2|E| \\ q_{n-2} &= \lambda_1\lambda_2 + \lambda_1 \lambda_3 + \dots + \lambda_{n-2} \lambda_{n-1} \\ q_{2} &= \lambda_1 \dots \lambda_{n-2} + \lambda_1 \dots \lambda_{n-3} \lambda_{n-1} + \dots + \lambda_2 \dots \lambda_{n-1}\\ q_{1} &= \lambda_1 \dots \lambda_{n-1} \\ \end{align}$$

Since a spanning forest with n–1 components corresponds to a single edge, the k = n – 1 case states that the sum of the eigenvalues of Q is twice the number of edges. The k = 1 case corresponds to the original Kirchhoff theorem since the weight of every spanning tree is n.

The proof can be done analogously to the proof of Kirchhoff's theorem. An invertible $(n-k) \times (n-k) $ submatrix of the incidence matrix corresponds bijectively to a k-component spanning forest with a choice of vertex for each component.

The coefficients $q_k$ are up to sign the coefficients of the characteristic polynomial of Q.

title: Kirchhoff's theorem


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Talk:Band of the 10th of December

This stub is a copy of, which uses the Creative Commons Share Alike-Attribution license 2.0. I'm not an expert on whether that's compatible with the GFDL, and a quick search of the wikipedia namespace wasn't helpful. 68.81.231.127 23:30, 12 Dec 2004 (UTC)

 * I guess that explains the Marxist jargon. P4k 04:42, 9 January 2007 (UTC)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Talk:Band of the 10th of December


text:
File:Los amantes del círculo polar poster.jpg

Summary
Poster for the film 'Los amantes del círculo polar'


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Huntingdon, Quebec

Huntingdon is a small town in Huntingdon County in the Haut-Saint-Laurent Regional County Municipality, and the Montérégie region of the province of Quebec, Canada. The population as of the 2021 Canadian census was 2,556. The town is 75 km southwest of Montreal, and 15 km from the border with New York State.

History
The town was settled by British soldiers after the War of 1812 and the fertile land in the area led to a successful farming economy. Once the fear of attack from the Americans was gone, in the 1820s businessmen established lumber and grist mills on the banks of the Châteauguay River.

During the first few decades of the 20th century, when transport from major urban centers to the outlying rural areas became economically feasible, the textile industry began expanding at a rapid rate in various towns throughout the province of Quebec. By the 1930s, Huntingdon was home to a small but thriving textile industry founded by Alex Fawcett & Hiram Leach as Leach Textiles. After World War II, entrepreneurs François Cleyn and Alec Tinker acquired the textile businesses in Huntingdon and built their company, Cleyn & Tinker Limited, into one of the most successful woolen mills in all of Canada. In Huntingdon, the business expanded to five interconnected operations around the town. The decades of the 1950s through to the early part of the 1970s saw the town prosper and the company acquire subsidiaries in Sherbrooke, Quebec and in Castlecomer, Kilkenny, Ireland.

Recent history
Huntingdon was also home to Huntingdon Mills (Canada) Ltd., another textile business and a significant employer in the town. In December 2004, the company filed for bankruptcy protection and announced they would have to close, putting more than 215 employees out of work. Cleyn & Tinker too announced it would be closing its operations in the town in April 2005. Shortly after the announcement, some of the company's assets and supply contracts were acquired by the Greensboro, North Carolina based International Textile Group, Inc. who have a partnership with China Ting Group, a textile manufacturer based in Kabul, Afghanistan. On January 28, 2005, Mayor Stéphane Gendron announced that the town was purchasing the five textile plants that were closing with the expectation that they could be sold to new businesses.

The small town had to deal with a substantial increase in teen vandalism. In August 2004 a controversial municipal bylaw went into effect that placed a 10:30 p.m. to 6:00 a.m. curfew on unsupervised children aged 15 and under. The controversial bylaw held parents responsible for their children's activities through fines if a child was caught in violation of the curfew. After parents filed a legal action to have the bylaw overturned, the Council suspended application of the bylaw.

Demographics
In the 2021 Census of Population conducted by Statistics Canada, Huntingdon had a population of $2,556$ living in $1,202$ of its $1,273$ total private dwellings, a change of NaN% from its 2016 population of $2,444$. With a land area of 2.77 km2, it had a population density of in 2021.

Government
Huntingdon's mayor is Andre Brunette. At the federal level, Huntingdon is part of the Salaberry—Suroît riding and is represented by Claude DeBellefeuille of the Bloc Québécois. Provincially, it is part of the electoral district of Huntingdon and is represented by Claire IsaBelle of the Coalition Avenir Québec.

List of former mayors:

 * Robert Brown Somerville (1848–1852)
 * John Morrisson (1852–1858)
 * Alexander Anderson (1858–1864)
 * Sitt Schuyler (1864–1866)
 * James Fortune (1866–1870)
 * Daniel Shanks (1870–1872)
 * Alexander Cameron (1872–1887, 1895–1898)
 * Daniel Boyd (1887–1893)
 * F. H. Henderson (1893–1895)
 * R. N. Walsh (1898–)
 * Andrew Philps (1904–1910)
 * Robert Crawford (1910–1913)
 * Thomas B. Pringle (1913–1922)
 * Dennis James O'Connor (1922–1931)
 * Walter Brown (1931–1933)
 * Gilbert Daniel Faubert (1933–1943)
 * Stanford Mc Nair (1943–1947)
 * Achille Picard (1947–1949)
 * Léo Capiello (1949–1959, 1965–1971)
 * Paul Lefebvre (1959–1965)
 * Claude Pilon (1971–1979)
 * Gérald Brisebois (1979–1995)
 * André Brunette (1995–2003)
 * Stéphane Gendron (2003–2013)
 * André Brunette (2013–present)

Transportation
The CIT du Haut-Saint-Laurent formerly provided commuter and local bus service, until it was cut back to Ormstown and Sainte-Martine. Current service is provided by the Haut-Saint-Laurent regional county municipality.

Media
The town is served by a fortnightly English newspaper, The Gleaner, with a French section called, Le Gleaner. It was founded in 1863 by Robert Sellar (1841-1919) under the banner Canadian Gleaner, changing its name to the Huntington Gleaner in 1912. The Huntingdon Gleaner was owned by various family businesses for most of its history. Even though it was technically a private business, local ownership conveyed the title of ‘community newspaper’ as is typical across Canada. Eventually, the Huntingdon Gleaner added a French language section in 1993 called La Source (back-to-back format) and became known as The Gleaner/La Source. As consolidation in the print media began at the turn of this century, The Gleaner/La Source was sold by the local owner to what became a series of re-sales to various media chains: Les Hebdos Montérégiens in 1985, Quebecor in 2011 and finally Transcontinental in 2013. In 2015, The Gleaner/La Source ceased publication as a standalone newspaper, with The Gleaner becoming an 8-page insert in the regional free-distribution weekly Le Journal St-Francois (Valleyfield), and La Source being closed completely. In 2017, Transcontinental sold Le Journal St-Francois (including The Gleaner) to a regional media company, Gravité Média. In 2018, Gravité Média reached out to the English-speaking community in the Châteauguay Valley to see if there was any interest in acquiring the title. Rather than simply close The Gleaner, Gravité Média wanted to respect the heritage integral to the publication and provide the opportunity for the English-speaking community to continue to be served by a community newspaper. In November 2018, a public meeting was held in Ormstown, along with representatives from Gravité Média, to discuss the possibilities surrounding the community acquiring the rights to continue publishing The Gleaner.

From that meeting, a “Future of the Gleaner” steering committee was formed, followed shortly by the establishment of a non-profit organization the Chateauguay Valley Community Information Services and discussions were held with Gravité Media to acquire the assets of The Gleaner (title, web domain,  etc.) and a transfer agreement was signed in May 2019. In June 2019, The Gleaner was re-launched with a souvenir print version and a new website, followed by monthly editions in August, September, October and November 2019 and a fortnightly edition stating in January 2020.

Sport
Huntingdon was the midway point of the Boston–Montreal–Boston cycling event.

title: Huntingdon, Quebec


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Bill Drayton

William Drayton (born 1943) is an American social entrepreneur. Drayton was named by U.S. News & World Report as one of America's 25 Best Leaders in 2005. He is responsible for the rise of the phrase "social entrepreneur", a concept first found in print in 1972.

Drayton is the founder and current chair of Ashoka: Innovators for the Public, a 501(c)(3) organization dedicated to finding and fostering social entrepreneurs worldwide. Drayton also chairs two other 501(c)(3) organizations, namely Youth Venture and Get America Working!

According to Drayton's philosophy, social entrepreneurs are individuals with innovative solutions to society's most pressing social problems. To quote Drayton, "Social entrepreneurs are not content just to give a fish or teach how to fish. They will not rest until they have revolutionized the fishing industry."

He was elected a Member of the American Philosophical Society in 2019.

Early years
Drayton's mother emigrated to the United States from Australia. His father was an American who became an explorer. His ancestors were some of the earliest anti-slavery abolitionist and women's leaders in the U.S. Drayton was born in 1943 in New York City.

Drayton attended high school at Phillips Academy, where he established the Asia Society, which soon became the school's most popular student organization. He attended Harvard where he received his Bachelor of Arts degree in 1965, where he created the Ashoka Table, bringing in prominent government, union, and church leaders for off-the-record dinners at which students could ask "how things really worked". Drayton entered Balliol College, Oxford and received a Master of Arts degree in 1967. He attended Yale Law School where he received his Juris Doctor in 1970. At Yale Law School, Drayton founded Yale Legislative Services, which, at its peak, involved a third of the law school's student body.

Career
Drayton became a manager and management consultant, working for McKinsey & Company as a consultant for almost ten years.

During the administration of President Jimmy Carter (1977–1981), Drayton was an Assistant Administrator of the Environmental Protection Agency where he launched emissions trading, among other reforms. He founded the group Save EPA after he left.

Drayton has served as a visiting professor at Harvard University and Stanford University.

Awards
Drayton has received many awards and acknowledgments for his achievements. He was elected one of the early MacArthur Fellows for his work, including the founding of Ashoka: Innovators for the Public.

The American Society of Public Administration and the National Academy of Public Administration jointly awarded him their National Public Service Award and he has also been named a Preiskel–Silverman Fellow for Yale Law School and is a member of the American Academy of Arts and Sciences.

On May 25, 2009, Drayton was awarded an honorary degree, Doctorate of Humane Letters, by Yale University at commencement.

David Gergen has called Drayton the "godfather of social entrepreneurship." And in 2008, Drayton was named a "visionary" as one of Utne Reader magazine's "50 Visionaries Who Are Changing the World".

In 2011, Drayton won Spain's prestigious Prince of Asturias Awards for international cooperation for his work promoting entrepreneurs. The prize foundation described him as a "driving force behind the figure of social entrepreneurs, men and women who undertake innovative initiatives for the common good".

Within the next two weeks, Drayton also accepted the John W. Gardner Leadership award, "established in 1985 to honor outstanding Americans who exemplify the leadership and the ideals of John W. Gardner", and the World Entrepreneurship Forum's Social Entrepreneur Award.

In 2012, Drayton was named an inaugural recipient of Middlebury College's Center for Social Entrepreneurship Vision Award, in recognition of the impact of his contributions to the field of social entrepreneurship.

title: Bill Drayton


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File:Katzs salamis.jpg

Street window at Katz's Deli. Photo/upload by J. Stander.

title: File:Katzs salamis.jpg


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Wikipedia:Articles for deletion/Portia

Portia
Portia was proposed for deletion. This page is an archive of the discussion about the proposed deletion. This page is no longer live. Further comments should be made on the article's talk page rather than here so that this page is preserved as an historic record. The result of the debate was keep.

Delete. If we're getting pokemon deleted as fancruft, certainly something like this should certainly be deleted as well. birdboy2000
 * Yeah, Shakespeare and Pokemon are basically interchangable. Keep, obviously. And last I heard Pokemon was not getting deleted, in any form. -R. fiend 23:55, 12 Dec 2004 (UTC)
 * Keep. Putting this on VfD is just insane.--Calton 23:57, 12 Dec 2004 (UTC)
 * Keep but the point is that keeping this and deleting 'notable' -mons is based on a subjective value judgement, one which I don't think an encylopedia should be making for its readers. Kappa 00:29, 13 Dec 2004 (UTC)
 * Keep. I wouldn't advise it as an ultimate notability test, but having a ball of rock about the size of Great Britain named after you probably serves even in the absense of anything else. I wouldn't argue that any Shakespearean character is notable - but there's not many who are more notable than her and still fictional. Note, incidentally, that The Merchant of Venice only has seperate pages for two characters; there is already restraint in the creation of these. (Her and Shylock, which at a guess are the most notable ones - it'd be hard to argue Shylock wasn't encyclopedic). Oh - incidentally, even were a page on Portia the heroine invalid, this page would still have to exist - if nothing else, as a redirect for the moon (inherently encylopedic) and the genus of spiders (which are probably also so). Voting for deletion, in this case, would just be silly. Shimgray 01:08, 13 Dec 2004 (UTC)
 * Oh, and I couldn't resist...
 * PORTIA: Of a strange nature is the suit you follow; (IV.1) Shimgray 01:13, 13 Dec 2004 (UTC)

 * Keep Do not disrupt Wikipedia to make a point. --[[User:Tony Sidaway|Tony Sidaway|Talk]] 01:33, 13 Dec 2004 (UTC)
 * Keep Pokemon may become regarded as Shakespeare, but it'll take a while. Urhixidur 02:24, 2004 Dec 13 (UTC)
 * Keep. Subjectivity is inherent in deciding what makes the cut and what doesn't, both in standard encyclopedias and on Wikipedia. We try to set up as many objective criteria as possible, but it is still a subjective process. Portia is significant not only for her Shakespeare role, but also especially for the astronomical and taxonomic significance. — [[User:Knowledge Seeker|Knowledge Seeker দ (talk)]] 04:02, 13 Dec 2004 (UTC)
 * Jesus Christ, keep. Is anyone tracking the increasing number of abusive listings lately?  There really needs to be a system in place to delist these bogus VfDs.  —[[en:RaD Man|RaD Man (talk)]] 05:20, 13 Dec 2004 (UTC)
 * There is discussion of such a method here. Joyous 00:05, Dec 14, 2004 (UTC)

 * Actually, I have to say that I think the deletability of most VfD listing has increased in recent months. Oh, and keep this by the way; we should only be so lucky as to have individual Pokemon deleted, and Shakespeare is in quite a different league. - RedWordSmith 21:12, Dec 13, 2004 (UTC)
 * I understand what you're getting at, but I think you could at least have chosen something borderline to make your point. This is about as subtle as a brick. Keep. Shane King 05:24, Dec 13, 2004 (UTC)

 * Keep: This is silly, of course, but I can provide a good guide for the difference between fancruft and non.  Does the subject ever appear outside of its fictive context and therefore require an encyclopedia to explain it?  In the case of Portia, you bet.  She's referred to all over the place.  In the case of Porkemon or Pigjuzumon or whatever, no.  If you're watching a contemporary movie, you might well hear some character say, "I have the choices of Portia," or you might encounter her name in "A Fish Called Wanda" and need to know what it means.  Geogre 05:36, 13 Dec 2004 (UTC)
 * Sorry but yes. See here.  Pokemon fans rejoice!  According to Geogre, Pikachu has evolved beyond fancruft.  The Steve  08:56, Dec 14, 2004 (UTC)
 * Pikachu has. I'd have said that anyway.  Now, about every other card, with lovingly obsessive comments, the "cities" with gyms, the power crystals, magic wands, and all the rest....  Pac-Man is beyond fancruft, but the names of the little guys who chase him, Inky, Blinky and something else, aren't.  Geogre 19:19, 14 Dec 2004 (UTC)
 * Keep. The point being made is perfectly valid, although Shakespeare characters are of course more notable than Pokemon characters. They are alike in that they are all culturally notable—in the sense that millions are familiar with them and they are integral to things that are familiar to millions more—but different in that Shakespeare has gained cultural respectability while Pokemon is considered a silly child's game. I consider only notability in my votes, not respectability. And I don't object to the listing, either. Sometimes it's good to make a point. Everyking 06:18, 13 Dec 2004 (UTC)
 * Keep. The quality of mercy is not strain'd, It droppeth as the gentle rain from heaven, Upon the place beneath. It is twice blest; It blesseth him that gives and him that takes. Portia's famous speech from the Mechant of Venice. I have added that plus the role being one of Shakespeares most notable romantic heroines. In addition, I have added some of the notable actresses that have played the part, the moon of Uranus, the reference from Rumpole of the Bailey, and the New England School of Law being known as the Portia Law School from 1908 to 1969. I even added in something from the mirror universe of Star Trek. I wasn't aware of the Fish called Wanda reference other than Archie Leach's daughter being called Portia so I can add that as well. In addition, the article also mentioned the role of Portia as Brutus's wife in ''Julius Caesar and I have added some od the actresses that have played that role. Capitalistroadster 09:36, 13 Dec 2004 (UTC)
 * Archie Leach's daughter is named Portia, and that's all you get, directly. Otto says, to Wanda, that he thinks it's cool that they named their daughter after a car.  The joke is, of course, that they didn't, and we, in the audience, need to know whom they did name her for.  I brought it up to suggest why Portia needs a stand-alone article as opposed to a spot in a Shakespeare's heroines article (and therefore why DigimonZ With Flame Gun needs to be merged into an article on the fiction as opposed to broken out as a solo article).  Geogre 14:02, 13 Dec 2004 (UTC)
 * Keep. Ridiculous listing IMO, does its cause no good at all and makes Wikipedia look silly. But the easiest thing is just to let the process take its course. Andrewa 11:12, 13 Dec 2004 (UTC)
 * Keep. Yet another example of Wikipedia being disrupted to make a point.  [[User:GRider|GRider\talk]] 17:19, 13 Dec 2004 (UTC)
 * Keep. Certainly notable. Fire Star 17:33, 13 Dec 2004 (UTC)
 * Uh, lessee...totally neologistic characters created by the committee of a Japanese electronics conglomerate versus a character from the most important author in the history of English literature. Do I really have to vote keep article and run the individual responsible for listing this through RfC? - Lucky 6.9 01:23, 14 Dec 2004 (UTC)
 * What would that serve? Portia is just another fictional character, no matter how great her author. Take the point, smile and move on. BTW, the Pokemons are probably more widely known these days. Dr Zen 03:11, 14 Dec 2004 (UTC)
 * No, she's not "just another fictional character." She's one of the lead characters in the story.  That's why she's notable enoough for an article, and her servants Balthazar and Stephano aren't, despite being created by the same author.  And if someone did create the Balthazar and Stephano articles, they'd soon be deleted as fancruft.  Keep.  P Ingerson 12:34, 17 Dec 2004 (UTC)
 * Good point. I just think there are better ways to get a point across.  Still, quite a lively discussion, eh?  Smiling... - Lucky 6.9 00:17, 15 Dec 2004 (UTC)
 * BTW, the Pokemons are probably more widely known these days. Only if your only point of reference is the opinions of nine-year-olds. -- GWO
 * Well, dude, frankly, intellecksherals like yourself are most likely outnumbered by nine-year-olds.Dr Zen 23:59, 14 Dec 2004 (UTC)
 * Keep. —tregoweth 02:25, Dec 14, 2004 (UTC)
 * Keep. Kappa thinks we should not make value judgements. (Like, say "Kappa's opinion is moronic")  We have notability requirements : the plays of Shakespeare are one of the key cultural reference points in the Anglophone world (and beyond).  Pokemon is a recent children's fad animation. Shakespeare will be being performed in 200 years, Pokemon won't.  That's not a value judgement, its bloody obvious to anyone who isn't a complete imbecile. -- GWO
 * So which parts of "recent children's fad animation" are reasons for deletion? It seems to me that children deserve to be served by encyclopedias as much or more than adults do. Animations are unworthy? Stage plays were regarded as inferior entertainment in their time. "Recent... fad" as a reason for deletion implies that either: you can confidently predict the future, which seems hubristic, or that you want to delete material now, and then possibly recreate that material if your prediction turns out to be wrong, which seems inefficient at best. Kappa 15:40, 14 Dec 2004 (UTC)
 * So which parts of "recent children's fad animation" are reasons for deletion? Words one and three will do the trick. --[[User:Tony Sidaway|Tony Sidaway|Talk]] 02:21, 15 Dec 2004 (UTC)
 * I think just being notable for any length of time is adequate. Where are you going to draw the line? Still notable after five, ten, 20, 50, 500 years? Oh, we're going to have to delete your article now, but if it can stay notable for a little while longer, then we'll let you write it over again. I say, if it's notable today, or it was notable yesterday, that's good enough. Everyking 02:56, 15 Dec 2004 (UTC)
 * Keep. Character is well-known outside the context of the play. (Her conundrum of the three chests is also part of common folklore and deserved to be part of this article too). Gdr 01:13, 2004 Dec 16 (UTC)
 * Keep Portia, delete the Pokémons.Martg76 04:48, 17 Dec 2004 (UTC)
 * Keep -- As someone who just recently deleted a sizable section on the Cat page devoted to discussing which Pokemon characters were somewhat similar to cats, it's pretty clear that the Pokemania has been spreading like a disease through this encyclopedia and needs to be reigned in. Shakespeare doesn't need to be reigned in. This character has survived the test of time, Pokeman likely will be nothing but a bad dream in another decade. DreamGuy 21:58, Dec 17, 2004 (UTC)

This page is now preserved as an archive of the debate and, like some other VfD subpages, is no longer 'live'. Subsequent comments on the issue, the deletion or on the decision-making process should be placed on the relevant 'live' pages. Please do not edit this page.

title: Wikipedia:Articles for deletion/Portia


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Lovers of the Arctic Circle

Lovers of the Arctic Circle (Los amantes del círculo polar), also known as The Lovers from the North Pole, is a 1998 Spanish romantic drama film written and directed by Julio Médem and starring Najwa Nimri and Fele Martínez. It won two Goya Awards in 1999.

The film tells the story of Otto and Ana (whose names are palindromes), from their chance meeting outside school at the age of 8, until they meet again in their 20s in Lapland within the Arctic Circle, under the midnight sun. The themes developed in the film form an important part of Julio Medem's universe, and can be found in his other movies; these include love, death, destiny, nature, the circle of life and the coincidences in life. It received favorable critical reviews.[1]

Plot
The movie (told from the point of view of the two main characters), opens with Otto (Fele Martinez) hanging from a tree by a parachute after surviving a fateful plane crash. In voiceover he reflects on how he met Ana (Najwa Nimri), his stepsister and secret lover.

17 years before, when Ana and Otto were 8, Otto first sees Ana while rushing to retrieve a soccer ball in the forest outside their school, and is smitten immediately. Ana's voiceover reveals that she was also immediately enamored, but nothing is spoken. She had run into the forest in grief over her father's death and at first she thinks Otto might be her father's reincarnation, but she dismisses the idea after studying her father's photo in an album and finding absolutely no resemblance between them.

The next morning Otto writes a question about love on dozens of paper airplanes and sends them flying over the schoolyard. They're read by everyone, including Ana's mother Olga and Otto's father Álvaro, who meet for the first time while commenting on this question. After exchanging a few words, Álvaro offers Olga and her daughter a ride.

Otto hears his father yelling his name, and runs to the car. When he opens the car door, he's shocked to see Ana in the back seat. She greets him warmly and openly; through her point of view we learn that she knows his name from his father's yelling and that she's surprised and delighted to see him again. They ride in the back seat. While their parents talk, Otto's voiceover reveals that he's hopelessly in love with Ana and wonders how she feels about him.

Neither child has siblings; Olga is a widow, and Otto's parents are divorced. His mother Yolanda isn't taking that too well. Otto feels sorry for her, but he is thrilled when his father marries Ana's mother: he will be close to his one true love.

The story moves forward several years. The two children are now in their middle teens, their unprofessed love fanatically hidden from their parents.

Otto's mother has never gotten over her divorce and Otto is a comfort to her. He's concerned about her welfare and feels responsible for keeping her happy, but his longing for Ana overpowers him.

Desire finally eclipses responsibility, and Otto moves in with his father, desperate for Ana's love. One night they're doing homework together and they discuss Finland, the Arctic Circle, and the Midnight Sun. They fall silent and Ana rests her head on Otto's chest and listens to his heartbeat. They make out.

Soon after, during a family barbecue, Ana passes Otto a note inviting him to her bedroom. That night he goes to her. At last they confront their feelings and become lovers.

Several more years pass and we see that they've succeeded in keeping their affair a secret, in spite of the fact that they're conducting it right under their parents' noses. However, Yolanda has sunk deeper into depression since Otto's departure. Finally, feeling abandoned by both husband and son, she commits suicide. Otto, guilt-ridden and bereaved, leaves his father's house one morning without saying a word, and essentially disappears. In utter despair, Ana locks herself in her room and cries, refusing to answer when her mother asks her what's wrong. She leaves home. Becomes a schoolteacher.

Time passes. Otto falls into a series of fatuous affairs. During one of them, the subject of his mother comes up. He tells the girl "She died of love" and when the girl asks "How does one die of love?" he answers, "She died abandoned."

Ana and Otto almost meet again in a park. They arrive separately and sit with their backs to each other, each unaware of the other's presence. Otto sits alone; Ana is approached by a man who wants to talk to her. All they would need to do is turn around to see the other sitting there, but this never happens and it's clear that something karmic has been shattered.

Ana begins a relationship with the man in the park. Meanwhile, her mother Olga is seduced away from Álvaro by another man, also named Álvaro, and ends their marriage. Otto returns home to find Ana and Olga gone and his father distraught over Olga leaving him.

Running through the story like a thread is the subplot of how Otto got his name:

There was a German fighter pilot during WWII named Otto and related to Yolanda, whose plane crashed in Finland. He fell in love with a woman.

The other Otto understands that because he has left Ana, he has been left without a destiny. He becomes a pilot like his namesake and flies to Finland, a twist of fate which Olga cheerfully communicates to Ana via a video. Soon after, Ana's affair with the man in the park turns dangerously sour and she's forced to get away from him. Olga's lover knows someone who has a cabin in Finland: it's none other than the man for whom Otto was named, the German pilot whose plane crashed during WWII. Olga's lover makes clear that the cabin is just sitting there empty and that the German pilot would willingly let Ana use it until the crisis with her lover blows over.

Ana accepts, and writes a letter to her stepbrother: She wants them to meet in Finland. The time has come to reclaim their love. Flying to the cabin, Ana looks out and sees Otto's cargo plane, but doesn't even think that it might be his. Almost simultaneously, Otto looks out the window of his cargo plane and sees the 747 Ana is on, but is equally oblivious.

Ana arrives at the cabin, and sits outside in a straight back chair, waiting for Otto to arrive. When he doesn't, she panics.

Meanwhile, Otto is hanging from a tree, having survived a plane crash just like his namesake, and getting his parachute caught in the branches... Bringing us to the beginning of the film.

Hearing that a cargo plane has crashed, Ana frantically tries to find out if it was Otto's. Tearing through the local newspaper looking for clues, gets hit by a truck on her way across the street. By this time Otto has been rescued and hitched a ride with his rescuers.

There's a final, two-part epilogue:

In the first part, Ana crosses the street instead of getting hit by the truck. She runs up the stairs of an apartment building and is greeted by the German pilot who tells her that someone inside the apartment is waiting for her. She goes inside and sees Otto who's smiling warmly. They exchange soft words, and she embraces him, making it the perfect reunion. Until it's seen that Ana's eyes are wide open and dilated and that Otto's face is reflected in the lenses.

In the second part, Otto and his rescuers have stopped at an intersection. Otto, seeing Ana sprawled on the pavement, gets out of the car and runs to her. It then cuts to their reunion (which is only a dream), and it's revealed that Otto's face in Ana's eyes is the reflection of him leaning over her as she sees him one last time before dying.

We see a shot of Otto's destroyed cargo plane in the snow.

Production
Lovers of the Arctic Circle was shot in Madrid and in various locations in Finland.

Julio Medem based part of the film on his own experience of unrequited teenage love for his next door neighbor. He also included a reference to his Basque mother and German father in a scene in which a Basque farmer rescues a stranded German paratrooper. Medem said this was "a way of bringing together the two sides of my family."

Awards
The film was nominated for four Goya Awards and won for Best Editing and Best Original Score. Julio Medem also received the Audience Award at the 2000 Athens International Film Festival and the Audience Award for Best Latin Film at the Gramado Film Festival. The film also won an Ondas Award for Best Spanish Film and Najwa Nimri won for Best Actress.

title: Lovers of the Arctic Circle


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Edgar Foshee

Sergeant Major Edgar Foshee, a devout anti-communist, served as a combat medic in the U.S. Army Special Forces. His former wife Thuong Nguyen Cuc Foshee was held without formal charge by the government of Vietnam starting in September 2005. She was eventually convicted of terrorism and returned to the United States in November 2006 after her early release for medical problems.

Biography
In 1974, he retired from the United States Army, and later retired as an agent from the Central Intelligence Agency (CIA). He had served in Vietnam with both organizations, assisting the South Vietnamese government against the Communist North Vietnamese Army and their Viet Cong agents.

He owned a construction company until 1980, and retired with his wife to Florida.

On April 30, 1995, he was appointed Chairman of the International Committee of an exiled anti-communist organization known as The Government of Free Vietnam.

Quotes

 * "I do hope that the Vietnamese Community Abroad quickly identifies the malicious motive of the Viet Cong."
 * "Vietnam is sending out secret agents to disrupt the motivation of the Vietnamese Community Abroad."
 * "Mr Nguyen Huu Chanh and the Government of Free Vietnam are motivated individuals determined to fight against the VCs to the end."

title: Edgar Foshee


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Microsoft Media Server

Microsoft Media Server (MMS), a Microsoft proprietary network-streaming protocol, serves to transfer unicast data in Windows Media Services (previously called NetShow Services). MMS can be transported via UDP or TCP. The MMS default port is UDP/TCP 1755.

Microsoft deprecated MMS in favor of RTSP (TCP/UDP port 554) in 2003 with the release of the Windows Media Services 9 Series, but continued to support the MMS for some time in the interest of backward compatibility. Support for the protocol was finally dropped in Windows Media Services 2008.

Microsoft still recommends using "mms://" as a "protocol rollover URL". As part of protocol rollover a Windows Media Player version 9, 10, or 11 client opening an "mms://" URL will attempt to connect first with RTSP over UDP and if that fails it will attempt RTSP over TCP. After an RTSP attempt fails, Windows Media Player versions 9 and 10 will attempt MMS over UDP, then MMS over TCP. If using Windows Media Player 11 and an RTSP attempt fails, or if using a previous version of Windows Media Player and MMS fails, a modified version of a HTTP over TCP connection will be attempted. This modified version is referred to by some third parties as MMSH, and by Microsoft as MS-WMSP (Windows Media HTTP Streaming Protocol). The uniform resource identifier (URI) scheme  has also been proposed to be used for the unrelated Multimedia Messaging Service (MMS) protocol.

For several years developers of the SDP Multimedia download-tool reverse engineered the MMS protocol and published unofficial documentation for it. However, Microsoft finally released the protocol specification in February 2008.

title: Microsoft Media Server


text:
Wikipedia:Articles for deletion/Rosta

Rosta
Looks like a district in a city or province which is only significant for being the birthplace of a Persian explorer. Perhaps a merge and redirect to Isfahan (city) or Isfahan (province), whichever is appropriate? — [[User:Knowledge Seeker|Knowledge Seeker দ (talk)]] 23:36, 12 Dec 2004 (UTC)
 * It's hard to verify its existance on Google, but assuming it exists how is it different from any of the other geo-stubs in the board? If it's true, then keep Sabine's Sunbird 01:44, 13 Dec 2004 (UTC)
 * Keep; this needs expansion, not deletion. It may be a while before someone happens upon it with info to add, but the connection with Ahmad ibn Rustah ensures its notability if nothing else does.  -- Smerdis of Tlön 02:58, 13 Dec 2004 (UTC)
 * You're right; I believe I was in error in nominating this. I have tried to find more information, but thus far, I have been unsuccessful. I'll add a stub notice and remove this nomination. — [[User:Knowledge Seeker|Knowledge Seeker দ (talk)]] 03:31, 13 Dec 2004 (UTC)

title: Wikipedia:Articles for deletion/Rosta


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Kvitsøy Tower

Kvitsøy Tower is the name for the aerial tower of the 1200 kilowatt transmitter of the broadcasting company of Norway for the frequency 1314 kHz, which was built in 1981/82. Kvitsøy-Tower was a 117.5 metres high, free standing centre-fed half-wave antenna constructed of a grounded steel framework. Horizontal crossbars are located at its top and at a height of 67.5 metres above ground to support the cables for a medium wave aerial, which are strung parallel to the tower. The vertical cables hanging from the lower crossbar are fixed to the ground with anchors.

The Norwegian public broadcaster NRK switched off the Kvitsøy transmitter at 22:00 UTC on Friday June 30, 2006. For years, the station had been heard fairly reliably at night by DX'ers along the Atlantic Coast of North America making it one of the easiest European stations to hear. The mast was demolished on 31 May 2012.

title: Kvitsøy Tower


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Landspeeder

Landspeeders are fictional anti-gravity craft used through the Star Wars movies and Star Wars expanded universe. They are depicted both in civilian and military capacities, and several versions have been merchandised as toys and models.

Origin and design
Landspeeders first appear in Star Wars. Two of them—Luke Skywalker's (Mark Hamill) X-34 and a V-35—were designed by noted special effects artist John Stears and were fitted around cars. Skywalker's landspeeder was designed and built by Ogle Design around the chassis of a Bond Bug three-wheeler car. One of the major challenges the production crew faced was disguising the wheels to create the illusion that the craft was hovering. For certain shots, they shot from camera angles that masked the wheels; for long-distance shots, they used reflective material, gelatin on the camera lens, and shadow effects. A small blur could be seen under the speeder, which George Lucas called "The Force Spot" (stated in Special Edition Tape). Production designer Roger Christian used an angled mirror and a broom attached to the vehicle's underside to create, at certain angles, the illusion that the craft was hovering and kicking up dust. Star Wars creator George Lucas used digital technology to enhance the landspeeder effects in the Special Edition of A New Hope.

Industrial Light and Magic's (ILM) Doug Chiang designed the Naboo Flash speeder with a "race car look" while the Gian speeder's appearance is ILM's response to Lucas' request that the Naboo troops have "a pick-up truck with guns."

The landspeeder was put on display in the exhibit Star Wars: Where Science Meets Imagination that moved between various museums in 2008.

Depiction
Within the Star Wars universe, speeder is a generic term for any "repulsorcraft" or vehicle which uses anti-gravity repulsorlift technology to hover and fly above a planet's surface. Landspeeders more specifically use repulsor technology to hover just above the ground, while they cannot achieve any great height they are cheap and fast. Many different types of landspeeders exist in the Star Wars universe to fulfill a variety of roles, including for personal transport.

 * In Star Wars Film and Television
 * X-34 Landspeeder: In A New Hope, Luke Skywalker (Mark Hamill) pilots an X-34 landspeeder, which he later sells before leaving Tatooine to join the Rebel Alliance. Reference material identifies the X-34 as a civilian vehicle manufactured by SoroSuub Corporation.  At 3.4 m long, the X-34 can accommodate a pilot and passenger, while magnetic clamps behind the seating can accommodate droids or other cargo.  Other features include retractable windshield which can enclose the cockpit, terrain scanner and night-vision headlights.  With three turbine engines, it has a top speed of 250 kph and maximum altitude of 1 m.
 * Flash Speeder: Flash speeders appear in The Phantom Menace as one of several patrol vehicles used by the Royal Naboo Security Forces. Designed for street patrol and high-speed pursuit by the SoroSuub Corporation, the Flash speeder is 4.5 m long with seating for a pilot and passenger and maximum altitude of 2 m.  It is armed with a single pursuit/defense blaster on a 360° swivel mount.
 * Gian Speeder: Gian speeders appear in The Phantom Menace as another landspeeder used by the Royal Naboo Security Force. Unlike the Flash speeder though, reference material identifies the Gian speeder as a heavier vehicle only employed for tactical situations.  Also manufactured by the SoroSuub Corporation, the Gian has a top speed of 160 kph. Its narrower body makes it harder to hit from the front or rear at the expense of maneuverability and its tougher hull is reinforced with armor to withstand glancing hits.  Larger than the Flash speeder with a length of 5.7 m, the Gian speeder seats a pilot, gunner and two passengers.  Standard armaments include two side-mounted light repeating laser cannons, with the option of a hood-mounted heavy laser cannon.  Each weapon is independently powered in the event the speeder's main generator is damaged.
 * M-68 Landspeeder: The M-68 landspeeder first appears in Solo: A Star Wars Story when Han Solo (Alden Ehrenreich) and Qi'ra (Emilia Clarke) hijack one to escape the White Worms gang. Within the Star Wars universe, the M-68 is described as a popular street racing model manufactured by Mobquet Swoops and Speeders.  Nicknamed the "street blaster bolt", the M-68 has a top speed of 225 kph and is available in both hardtop and open-air models.
 * A-A4B Truckspeeder: When Han and Qi'ra attempt to flee the White Worms gang in Solo, they are pursued by Moloch in an A-A4B Truckspeeder. Described as a heavy, rugged design, the A-A4B was built in-universe by Trast Heavy Transports with armored caging over the driver's seat and front grille, turning the landspeeder into a batter ram during high-speed chases.

Cultural impact
Luke Skywalker's X-34 landspeeder was one of fifty fictional vehicles selected for display at the Petersen Automotive Museum's Hollywood Dream Machines exhibition which focused on the most significant or important vehicles to feature in the science fiction and fantasy genre. The X-34 was chosen not just for its role in the plot but also it's thematic contribution to the film.

Many Star Wars fans have been inspired to build "working" full-scale replicas of Luke's X-34 landspeeder. Daniel Deutsch built a drivable replica in 2007 using parts from an electric golf cart and fiberglass molding. The replica achieved fame when it was highlighted by former 'N Sync member Joey Fatone and rapper Kanye West. Celebrity YouTube inventor Colin Furze created another replica in 2019 in celebration of the release of Star Wars: The Rise of Skywalker. The only known full-scale metal model of the X-34, it was sold on eBay for £50,000, with all proceeds going to BBC’s ‘Children In Need’.

Landspeeders have served as a source of inspiration for Star Wars fans across artistic communities. Digital artist Brad Builds created a landspeeder version of the Pontiac GTO themed around Darth Vader. French photographer Renaud Marion reimagined 9 classic cars as landspeeders as part of a project called Air Cars. Reimagined models included the Porsche 356 and Aston Martin DB5.

Although they operate on different principles, flying cars are often compared to Star Wars landspeeders in popular media. The SkyDrive SD-03 flying car specifically was inspired in part by Luke Skywalker's landspeeder.

Landspeeders have featured heavily in Star Wars merchandising since their inception. Examples includes Lego models, a drivable Radio Flyer toy, and a cat bed.

title: Landspeeder