text:
Talk:Hann. Münden

Hi,

"Tillyschanze, and observation tower built by Count Tilly in 1626." That is wrong. The tower was built from 1881 to 1885 by citizen to remember the siege of the town by Count Tilly. look at the german Wiki: http://de.wikipedia.org/wiki/Hann._M%C3%BCnden#Sehensw.C3.BCrdigkeiten 92.76.124.157 (talk) 20:14, 7 July 2010 (UTC) Hi David,

The official name is Hann. Münden. Yes, it is the abbreviations for Hannoversch Münden. But the name is no longer Hannoversch Münden (partly because many thaugt Münden was a quarter of Hanover).

Official entries in governmental lists say that the City is called Hann. Münden since June 1990.

You won't want to change the entry of New York back to Nieuve Amsterdam, just because this was the former name of it, do you? Hi, 80.128.181.xxx (a name would be nice - no sarcasm intended)

I accept your point about the name used officially, and normally I'd put it under the official name unless there was one better known in English (no chauvinism there; it's just usual encyclopedia practice). In fact there is one - it's plain Münden, but I didn't propose reverting it to that out of respect for local wishes to the contrary, even though official names have no overriding right of precedence.

There are two problems here though. First, I think abbreviations should on principle be avoided in article titles (I've just similarly redirected from F.Y.R.O.M., which I'd imagine is meaningless to most people). Second, though, there's a language issue which interconnects to some extent: while the abbreviation "Hann." may be readily comprehensible to a German as representing Hannoversch, it's similarly meaningless in English (and of course it doesn't help that we spell it with one "n"). I wouldn't object to its use in German Wikipedia, but I just don't think it's helpful in the English version.

Finally, please take note of what I said about accents in article titles. I use umlauts in article texts, but in the title they make a real mess of article editing.

I'd like to know what the city's inhabitants call it in their daily speech: can you advise?

Regards - User:David Parker

Hello,

daily speech is a little difficult situation:

 * When asked by a stranger (someone not from Hann. Münden, that is) where I come from, I would tell him "from Hann. Münden, a little town half way between Kassel and Göttingen".
 * When telling my parents that I'm coming by train, I would ask them "could you please pick me up at the station in Münden at 8:45?".
 * Some older people, especially those not living in Hann. Münden any more, still say Hannoversch Münden.
 * The younger sometimes use the word "Ha-Mü".

Regarding titles, can I change those after creating the article?

Regarding "english name of the city", Münden does not appear very english to me, especially due to the two dots on top of the "u".

Best regards,  JeLuF Hi, JeLuF

If few inhabitants would really pronounce "Hannoversch", then I'll defer to your judgement (I didn't realise you were from there), though I still hate that "." in a title. We British would of course tend to put "Munden" or perhaps "Muenden", though some of us are very particular about the "ü". You can't change the title of an existing article as such: just start a new one, copy the text and add the old title to the "Page titles to be deleted" list here.

User:David Parker

The renaming in 1990 just changed Hannoversch to Hann. which has been already the name in earlier times. But the prefix is much older than 10 years. -- JeLuF 05:54 Dec 14, 2002 (UTC)

 * Hello, JeLuF - where did you get these informations? The official site of Hann. Münden states, that the name of the town was Münden until 1990: http://www.hann-muenden.net/spontan/geschi.htm#1900 (unfortunately German language only). I have read all the entries on this talk page, but I didn't find evidence for these statements on other www sites. The town's webiste itself also has the title "Hann. Münden", but it adds in brackets: ("Hannoversch Münden") - so they don't seem to have problems with this name, and I think, THEY should know how to call their own town. I will revert your last edit, since it seems to be obviously wrong to me. (Note: I just wrote an e-mail to the webmasters of the Münden website in order to definitely answer this question.) -- Cordyph

 * I'm a native of Hann. Münden. The town was called Hannoversch much before 1990. It has changed spelling several times. During the 80s Hannoversch Münden was often considered to be a part of Hanover, that's why the name was changed from Hannoversch Münden to Hann. Münden. BTW, www.hann-muenden.net is not the official homepage, it's a private homepage. I will revert your edits. -- JeLuF

 * Your last edit is fine, JeLuF. I'm sorry but I didnt' get, that you are a native of this town. It seemed too strange to me, that the inhabitants use an abbreviation, when pronouncing the name of their town. Be that as it may, I am now convinced. -- Cordyph

 * I'm working on some old church records from the 1658. In those, the town is called referred to as "Münden" and "Münden aus der Bluhm". brianfreud 16:32, 21 October 2021 (UTC)  — Preceding unsigned comment added by Brianfreud (talk • contribs)

Another almost local (from Göttingen, just 30km away). We would always call it "Hann.Münden. That's just its name, we would never think of it as an abbreviation (compare Bo'ness for a similar example in English, there are many more). Occasionally you would hear "Ha-Mü". Never Hannoversch Münden and never just Münden. The Göttingen dialekt has a tendency to blend 'i' and 'ü': it really becomes indistinguishable from Minden. 86.161.117.126 (talk) 21:55, 29 November 2021 (UTC)

Requested move

 * The following discussion is an archived debate of the . Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.

Move. Sorry, Pmanderson, but I kinda fail to see the point in the (appreciated, though) exercise. The town is small enough that verification of "English" usage becomes inconclusive (ergo Nuremberg vs. Nürnberg parallel doesn't apply), and the fact that it changed 3 spelling variants of the name through history, makes it even more inconclusive. So we might as well go after the official name. Duja ► 10:14, 29 January 2007 (UTC)

Hannoversch Münden → Hann. Münden — The town has changed its official name almost two decades ago, and the current article can't be moved to Hann. Münden (which is a redirect) by non-administrators. Hannoversch Münden is a deprecated old name, but not the current one to be used as per WP:NC. doco ( ☏ ) 14:03, 16 January 2007 (UTC)

Survey

 * Add  # Support   or   # Oppose   on a new line in the appropriate section followed by a brief explanation, then sign your opinion using ~ .  Please remember that this survey is not a vote, and please provide an explanation for your recommendation.

Survey - in support of the move

 * 1) Sure. "Hannoversch" is not in common use anymore. Kusma (討論) 08:36, 17 January 2007 (UTC)
 * 2) Support as nominator. doco ( ☏ ) 13:43, 21 January 2007 (UTC)

Survey - in opposition to the move

 * 1) Strongly oppose Violation of WP:NAME; move target not favored in English. Septentrionalis PMAnderson 22:37, 16 January 2007 (UTC)

Discussion

 * Add any additional comments:

How is the name read in German, "Hannoversch Münden or "Hann Münden" or is it simply "Münden?" —  AjaxSmack     19:02, 16 January 2007 (UTC)
 * There was a discussion at de:Hann. Münden about that. The outcome basically was that in normal speech, locals would say "Münden", the town would generally be called "HannMünden" in talk with non-locals, not spelling the dot, and occasionally "Hannoversch Münden" would be used.
 * Also, the charter of the town (can be found here) says in §1 "The name of the town is Hann. Münden.", so that is the official version in writing. --doco ( ☏ ) 19:57, 16 January 2007 (UTC)
 * Münden or Munden get far more English ghits than Hann. Münden; if it is unambiguous in writing, we should probably use it. (Presumably there is also English usage of Muenden.) More precise tests can be found at Naming conventions (geographic names), but I suspect they would give much the same result. Septentrionalis PMAnderson 20:13, 16 January 2007 (UTC)
 * Münden is ambiguous to Minden, which is why Münden got the "Hannoversch" in front of its name in the late 1800s to begin with. Also, your ghits request seemed to be slightly malformed. I get far less for this one than for this. —The preceding unsigned comment was added by Doco (talk • contribs) 20:31, 16 January 2007 (UTC).
 * I didn't search for Hannoversch Münden; I searched for Münden. I will agree the article should be moved, but not to the target proposed. ("Hanover" is included partly to ensure actual English, and partly to ensure that the hit is for this locality.) Minden is not a problem for a move to Münden; we don't disambiguate for pronunciation, just to have distinct pages. (There should be a dab header anyway.) Septentrionalis PMAnderson 21:00, 16 January 2007 (UTC)
 * I see several problems with that - first, the town -used- to be called either "Münden" or "Minden", with actual spelling varying wildly, but was renamed in the 19th century to "Hannoversch Münden", as it is situated on the Weser, just like Minden (which is a few 100 kilometres further upstream), and so the towns were regularly confused. The "Hannoversch" was chosen because the town was situated in the kingdom of Hanover at the time. This means you are likely to get many references for this town going by the name of "Münden" concerning events of the 19th century and before, but for any event after the 1880s, there will likely be "Hannoversch Münden". The town decided to rename itself to "Hann. Münden" in 1990 because nobody was spelling out the full name anyways - and it was always confused with being a borough of Hanover. So Hann. Münden is the official name (which we should use imo), Hannoversch Münden is the old name, and Münden is the old old name. Moving it to Münden would therefore constitute making the pre-1800s name the de facto name, and I think it'd be similar to moving New York to Nieuw Amsterdam, as someone said in the old discussion on this page. Also keep in mind that the "Hannoversch" is a proper noun, as the place has nothing to do with Hanover -per se-, but just had the tag added to enable people to differentiate it from Minden. (There are a few more places in Germany that work like that, for example Preußisch Oldendorf.) Therefore, of the three possibilities (keep at Hannoversch Münden, move to Hann. Münden as requested or move to Münden), the third option is the worst one in my opinion. (Although I don't mind a redirect.) --doco ( ☏ ) 21:33, 16 January 2007 (UTC)
 * It's more closely equivalent to moving Hannover to Hanover, if we had been unwise enough to accept the German official name for the city. Septentrionalis PMAnderson 21:41, 16 January 2007 (UTC)
 * Okay. *sigh* Everything in a nutshell again. The "Hannoversch" in Hannoversch Münden is a proper noun, as I've stated above. The place is called "Hann. Münden" since 1990. In legal documents, by the government, even on the railway signage and motorway exits. The place used to be called "Münden", but that name is rarely used outside the place itself anymore. Therefore, "Hann. Münden" is the legal and de facto name, with the Hann. being a proper noun. There is no English transcription for Münden. Which leaves us with: Hann. Münden. --doco ( ☏ ) 21:52, 16 January 2007 (UTC)
 * Of course Hannoversch is a proper adjective; I am not arguing for Hanoverian Münden. Perhaps I should have used Nuremberg as my exemplum, but I thought the neighboring town would be clearer. Münden and Munden are widely used in English, and either is, in English, unambiguous. Septentrionalis PMAnderson 22:40, 16 January 2007 (UTC)
 * WP:NC:CITY states: In absence of a common English name, the current local name of the city should be used.. Therefore, since Münden is the historical name of the city, not the current one, and since the city does not have a common English name like Hanover or Nuremberg, obviously the current local name needs to be used, which undisputedly is Hann. Münden. --doco ( ☏ ) 22:58, 16 January 2007 (UTC)
 * But there is a common, almost invariable, English name. See below. Septentrionalis PMAnderson 01:09, 17 January 2007 (UTC)

A parallel case
This is, in fact, the essential question: Do you think Hanover should be at Hannover?
 * In that case, local official usage is clearly Hannover and English usage is clearly Hanover. Septentrionalis PMAnderson 21:41, 16 January 2007 (UTC)
 * As mentioned above, "Hannoversch" is a proper noun. Preußisch Oldendorf isn't at Prussian Oldendorf either for the same reason. --doco ( ☏ ) 21:52, 16 January 2007 (UTC)
 * Proper adjective. Very well, do you think Nuremberg should be moved to Nürnberg, which is equally certainly the official name? Septentrionalis PMAnderson 22:35, 16 January 2007 (UTC)
 * Nuremberg has a common English name. Hann. Münden hasn't. --doco ( ☏ ) 22:58, 16 January 2007 (UTC)
 * That requires proof, which is not presented.  Please remember that many local names, like Paris or Berlin, are widely accepted in English. Similarly, the English name of Minden is Minden; fixed by the battle. So here, the statistics indicate that Münden is the  English proper name, as in the title of the 1911 Britannica's article on the subject. (This cites Henze: Führer durch Münden und Umwegung (Münden, 1900) so the use of unaccompanied Münden can't be that old, even in German; other book titles suggest it is consistent Wilhelmine usage. Similarly, Hann. Münden cites "Helmut Saehrendt: Hannoversch Münden. Wissenswertes aus der Geschichte der Stadt, sehenswertes in der Stadt, Hannoversch Münden 2002. ) The present Britannica's only mention of the place, under Weser River is " Formed near the city of Münden by the union of its two headstreams—the Fulda and the Werra...". Septentrionalis PMAnderson 01:07, 17 January 2007 (UTC)
 * Fine. The 1911 EB reference you cite is too old. See WP:NCGN where it says that sources should only be considered if they were published in 1993 or later (Obviously, this town has had its name changed in 1990, so try and find a reference to "Hann. Münden" in the 1911 EB - you won't!). The second example you cite is in German anyways, so that's irrelevant for this discussion. Here's a bunch of recent English-language published books backing the use of Hann. Münden as the regularly used name: Adventure Guide to Germany, Hunter Publishing Inc., 2005, Singing Sailors, York University (Toronto, Ont.), 2002, Rust Diseases of Willow and Poplar, CABI Publishing, 2005, The Rough Guide to Germany, Gordon McLachlan, 2004. All of these books are verifiable with Google Books, and I could come up with dozens more if I'd invest more than five minutes of research into this. As neither the EB nor Encarta seem to have proper articles about Hann. Münden, I'm afraid you'll have to accept these as reference for the modern(!) usage of the name and give up on insisting to use the archaic name. --doco ( ☏ ) 11:20, 17 January 2007 (UTC)

Data

 * 1) Encyclopedias (current; although WP:NCGN specifies 1993 because of the boundary changes in Eastern Europe; how this applies to Hanover is beyond me
 * 2) *Britannica 5 hits, all Münden
 * 3) *Columbia: 3 hits, two Hannoversch-Münden; one Münden
 * 4) *Encarta no hits for this location
 * 5) Scholarly seaches.
 * 6) *Scholar.google.com. 161 hits for Münden without Hann.; 136 hits for "Hann. Münden". All of the first page are street addresses, which WP:NCGN says to disregard.
 * 7) *Books.google.com. This has the problem of limiting to English hits. By including "Hanover" as a likely search term, I get 15 for Hann. Münden, and four of those are still in German; there are 420 for Münden without Hann., Of those 10 include Hannoversch.
 * 8) Histories and country studies.
 * 9) *The LC country study for Germany doesn't mention it.
 * 10) News sources
 * 11) *Lexis, gives 14 hits; 4 Hann. Münden or Muenden; 3 Hannoversch; 1 Hannoverisches; and 6 plain Münden
 * 12) *The BBC has one story and it uses Hannoversch Muenden
 * Septentrionalis PMAnderson 20:37, 17 January 2007 (UTC)
 * The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

The above data will show that "Hann. Münden" is used in English as often, relatively, as "Nürnburg" is, and in the same sources; hasty newspaper reports, and guidebooks. We should use English: Nuremburg, Hanover and Münden. Septentrionalis PMAnderson 23:34, 4 February 2007 (UTC)

As I recall (1980s-early naughts), we native speakers of English in Goettingen, when speaking English, used Hann. Muenden. This is in contrast to, e.g., Munich. I'd say that the town is basically unknown in GB, US, etc. and should have the entry under the German name: Hann. Muenden. Kdammers 11:40, 24 May 2007 (UTC)

title: Talk:Hann. Münden


text:
User:Huajie

|Huajie Liu| , Professor, Peking University.

|High Quality Botanical Images by Huajie Liu|, with 190 families of plants.

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

title: User:Huajie


text:
Shortest path problem

In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.

The problem of finding the shortest path between two intersections on a road map may be modeled as a special case of the shortest path problem in graphs, where the vertices correspond to intersections and the edges correspond to road segments, each weighted by the length of the segment.

Definition
The shortest path problem can be defined for graphs whether undirected, directed, or mixed. Here it is defined for undirected graphs; for directed graphs the definition of path requires that consecutive vertices be connected by an appropriate directed edge.

Two vertices are adjacent when they are both incident to a common edge. A path in an undirected graph is a sequence of vertices $$P = ( v_1, v_2, \ldots, v_n ) \in V \times V \times \cdots \times V$$ such that $$v_i$$ is adjacent to $$v_{i+1}$$ for $$1 \leq i < n$$. Such a path $$P$$ is called a path of length $$n-1$$ from $$v_1$$ to $$v_n$$. (The $$v_i$$ are variables; their numbering here relates to their position in the sequence and needs not to relate to any canonical labeling of the vertices.)

Let $$E = \{e_{i, j}\}$$ where $$e_{i, j}$$ is the edge incident to both $$v_i$$ and $$v_j$$. Given a real-valued weight function $$f: E \rightarrow \mathbb{R}$$, and an undirected (simple) graph $$G$$, the shortest path from $$v$$ to $$v'$$ is the path $$P = ( v_1, v_2, \ldots, v_n )$$ (where $$v_1 = v$$ and $$v_n = v'$$) that over all possible $$n$$ minimizes the sum $$\sum_{i =1}^{n-1} f(e_{i, i+1}).$$ When each edge in the graph has unit weight or $$f: E \rightarrow \{1\}$$, this is equivalent to finding the path with fewest edges.

The problem is also sometimes called the single-pair shortest path problem, to distinguish it from the following variations:
 * The single-source shortest path problem, in which we have to find shortest paths from a source vertex v to all other vertices in the graph.
 * The single-destination shortest path problem, in which we have to find shortest paths from all vertices in the directed graph to a single destination vertex v. This can be reduced to the single-source shortest path problem by reversing the arcs in the directed graph.
 * The all-pairs shortest path problem, in which we have to find shortest paths between every pair of vertices v, v'  in the graph.

These generalizations have significantly more efficient algorithms than the simplistic approach of running a single-pair shortest path algorithm on all relevant pairs of vertices.

Algorithms
Several well known algorithms exist for solving this problem and its variants.
 * Dijkstra's algorithm solves the single-source shortest path problem with non-negative edge weight.
 * Bellman–Ford algorithm solves the single-source problem if edge weights may be negative.
 * A* search algorithm solves for single-pair shortest path using heuristics to try to speed up the search.
 * Floyd–Warshall algorithm solves all pairs shortest paths.
 * Johnson's algorithm solves all pairs shortest paths, and may be faster than Floyd–Warshall on sparse graphs.
 * Viterbi algorithm solves the shortest stochastic path problem with an additional probabilistic weight on each node.

Additional algorithms and associated evaluations may be found in.

Directed acyclic graphs (DAGs)
An algorithm using topological sorting can solve the single-source shortest path problem in time $Θ(E + V)$ in arbitrarily-weighted DAGs.

Directed graphs with nonnegative weights
The following table is taken from, with some corrections and additions. A green background indicates an asymptotically best bound in the table; L is the maximum length (or weight) among all edges, assuming integer edge weights.

Directed graphs with arbitrary weights with negative cycles
Finds a negative cycle or calculates distances to all vertices.

All-pairs shortest paths
The all-pairs shortest path problem finds the shortest paths between every pair of vertices $v$, $v'$ in the graph. The all-pairs shortest paths problem for unweighted directed graphs was introduced by, who observed that it could be solved by a linear number of matrix multiplications that takes a total time of $O(V^{4})$.

Applications
Shortest path algorithms are applied to automatically find directions between physical locations, such as driving directions on web mapping websites like MapQuest or Google Maps. For this application fast specialized algorithms are available.

If one represents a nondeterministic abstract machine as a graph where vertices describe states and edges describe possible transitions, shortest path algorithms can be used to find an optimal sequence of choices to reach a certain goal state, or to establish lower bounds on the time needed to reach a given state. For example, if vertices represent the states of a puzzle like a Rubik's Cube and each directed edge corresponds to a single move or turn, shortest path algorithms can be used to find a solution that uses the minimum possible number of moves.

In a networking or telecommunications mindset, this shortest path problem is sometimes called the min-delay path problem and usually tied with a widest path problem. For example, the algorithm may seek the shortest (min-delay) widest path, or widest shortest (min-delay) path.

A more lighthearted application is the games of "six degrees of separation" that try to find the shortest path in graphs like movie stars appearing in the same film.

Other applications, often studied in operations research, include plant and facility layout, robotics, transportation, and VLSI design.

Road networks
A road network can be considered as a graph with positive weights. The nodes represent road junctions and each edge of the graph is associated with a road segment between two junctions. The weight of an edge may correspond to the length of the associated road segment, the time needed to traverse the segment, or the cost of traversing the segment. Using directed edges it is also possible to model one-way streets. Such graphs are special in the sense that some edges are more important than others for long-distance travel (e.g. highways). This property has been formalized using the notion of highway dimension. There are a great number of algorithms that exploit this property and are therefore able to compute the shortest path a lot quicker than would be possible on general graphs.

All of these algorithms work in two phases. In the first phase, the graph is preprocessed without knowing the source or target node. The second phase is the query phase. In this phase, source and target node are known. The idea is that the road network is static, so the preprocessing phase can be done once and used for a large number of queries on the same road network.

The algorithm with the fastest known query time is called hub labeling and is able to compute shortest path on the road networks of Europe or the US in a fraction of a microsecond. Other techniques that have been used are:

 * ALT (A* search, landmarks, and triangle inequality)
 * Arc flags
 * Contraction hierarchies
 * Transit node routing
 * Reach-based pruning
 * Labeling
 * Hub labels

Related problems
For shortest path problems in computational geometry, see Euclidean shortest path.

The shortest multiple disconnected path is a representation of the primitive path network within the framework of Reptation theory. The widest path problem seeks a path so that the minimum label of any edge is as large as possible.

Other related problems may be classified into the following categories.

Paths with constraints
Unlike the shortest path problem, which can be solved in polynomial time in graphs without negative cycles, shortest path problems which include additional constraints on the desired solution path are called Constrained Shortest Path First, and are harder to solve. One example is the constrained shortest path problem, which attempts to minimize the total cost of the path while at the same time maintaining another metric below a given threshold. This makes the problem NP-complete (such problems are not believed to be efficiently solvable for large sets of data, see P = NP problem). Another NP-complete example requires a specific set of vertices to be included in the path, which makes the problem similar to the Traveling Salesman Problem (TSP). The TSP is the problem of finding the shortest path that goes through every vertex exactly once, and returns to the start. The problem of finding the longest path in a graph is also NP-complete.

Partial observability
The Canadian traveller problem and the stochastic shortest path problem are generalizations where either the graph is not completely known to the mover, changes over time, or where actions (traversals) are probabilistic.

Strategic shortest paths
Sometimes, the edges in a graph have personalities: each edge has its own selfish interest. An example is a communication network, in which each edge is a computer that possibly belongs to a different person. Different computers have different transmission speeds, so every edge in the network has a numeric weight equal to the number of milliseconds it takes to transmit a message. Our goal is to send a message between two points in the network in the shortest time possible. If we know the transmission-time of each computer (the weight of each edge), then we can use a standard shortest-paths algorithm. If we do not know the transmission times, then we have to ask each computer to tell us its transmission-time. But, the computers may be selfish: a computer might tell us that its transmission time is very long, so that we will not bother it with our messages. A possible solution to this problem is to use a variant of the VCG mechanism, which gives the computers an incentive to reveal their true weights.

Negative cycle detection
In some cases, the main goal is not to find the shortest path, but only to detect if the graph contains a negative cycle. Some shortest-paths algorithms can be used for this purpose:

 * The Bellman–Ford algorithm can be used to detect a negative cycle in time $$O(|V||E|)$$.
 * Cherkassky and Goldberg survey several other algorithms for negative cycle detection.

General algebraic framework on semirings: the algebraic path problem
Many problems can be framed as a form of the shortest path for some suitably substituted notions of addition along a path and taking the minimum. The general approach to these is to consider the two operations to be those of a semiring. Semiring multiplication is done along the path, and the addition is between paths. This general framework is known as the algebraic path problem.

Most of the classic shortest-path algorithms (and new ones) can be formulated as solving linear systems over such algebraic structures.

More recently, an even more general framework for solving these (and much less obviously related problems) has been developed under the banner of valuation algebras.

Shortest path in stochastic time-dependent networks
In real-life situations, the transportation network is usually stochastic and time-dependent. In fact, a traveler traversing a link daily may experiences different travel times on that link due not only to the fluctuations in travel demand (origin-destination matrix) but also due to such incidents as work zones, bad weather conditions, accidents and vehicle breakdowns. As a result, a stochastic time-dependent (STD) network is a more realistic representation of an actual road network compared with the deterministic one.

Despite considerable progress during the course of the past decade, it remains a controversial question how an optimal path should be defined and identified in stochastic road networks. In other words, there is no unique definition of an optimal path under uncertainty. One possible and common answer to this question is to find a path with the minimum expected travel time. The main advantage of using this approach is that efficient shortest path algorithms introduced for the deterministic networks can be readily employed to identify the path with the minimum expected travel time in a stochastic network. However, the resulting optimal path identified by this approach may not be reliable, because this approach fails to address travel time variability. To tackle this issue some researchers use distribution of travel time instead of expected value of it so they find the probability distribution of total travelling time using different optimization methods such as dynamic programming and Dijkstra's algorithm. These methods use stochastic optimization, specifically stochastic dynamic programming to find the shortest path in networks with probabilistic arc length. The concept of travel time reliability is used interchangeably with travel time variability in the transportation research literature, so that, in general, one can say that the higher the variability in travel time, the lower the reliability would be, and vice versa.

In order to account for travel time reliability more accurately, two common alternative definitions for an optimal path under uncertainty have been suggested. Some have introduced the concept of the most reliable path, aiming to maximize the probability of arriving on time or earlier than a given travel time budget. Others, alternatively, have put forward the concept of an α-reliable path based on which they intended to minimize the travel time budget required to ensure a pre-specified on-time arrival probability.

title: Shortest path problem


text:
Von Neumann machine

Von Neumann machine may refer to:

 * Von Neumann architecture, a conceptual model of nearly all computer architecture
 * IAS machine, a computer designed in the 1940s based on von Neumann's design
 * Self-replicating machine, a class of machines that can replicate themselves
 * Universal constructor (disambiguation)
 * Von Neumann probes, hypothetical space probes capable of self-replication
 * Nanorobots, capable of self-replication
 * The Von Neumann cellular automaton

title: Von Neumann machine


text:
Bonnie Tyler

Gaynor Sullivan (née Hopkins; born 8 June 1951 ), known professionally as Bonnie Tyler, is a Welsh singer who is known for her distinctive husky voice. Tyler came to prominence with the release of her 1977 album The World Starts Tonight and its singles "Lost in France" and "More Than a Lover". Her 1977 single "It's a Heartache" reached number four on the UK Singles Chart, and number three on the US Billboard Hot 100.

In the 1980s, Tyler ventured into rock music with songwriter and producer Jim Steinman. He wrote Tyler's biggest hit "Total Eclipse of the Heart", the lead single from her 1983 UK chart-topping album Faster Than the Speed of Night. Steinman also wrote Tyler's other major 1980s hit "Holding Out for a Hero". She had success in mainland Europe during the 1990s with Dieter Bohlen, who wrote and produced her hit "Bitterblue". In 2003, Tyler re-recorded "Total Eclipse of the Heart" with singer Kareen Antonn. Their bilingual duet, titled "Si demain... (Turn Around)", topped the French charts.

Rocks and Honey was released in 2013 and features the single "Believe in Me", which she performed representing the United Kingdom at the Eurovision Song Contest 2013 in Malmö, Sweden. After reuniting with the producer David Mackay, she released Between the Earth and the Stars (2019) and The Best Is Yet to Come (2021).

Her work has earned her three Grammy Award nominations and three Brit Award nominations (including twice for British Female Solo Artist), among other accolades. In 2022, she was awarded an MBE in the Queen's Birthday Honours for services to music.

Early life
Tyler was born Gaynor Hopkins on 8 June 1951 in Skewen, Neath, Wales. Her father, Glyndŵr Hopkins, was a coal miner and serviceman in the Second World War, and her mother, Elsie Hopkins (née Lewis), was a former homemaker. She grew up in a four-bedroom council house with three sisters and two brothers. Her siblings had varied music tastes, exposing her to artists such as Elvis Presley, Frank Sinatra and the Beatles. Hopkins attended Rhydhir Comprehensive School in Neath, Wales. She left school, age 16, with no qualifications and began working in a grocery shop. Hopkins and her family were deeply religious Protestants. Her first public performance took place in a chapel as a child, singing the Anglican hymn "All Things Bright and Beautiful".

In April 1969, Hopkins was entered into a local talent competition by her aunt, and she came second to an accordionist. Inspired to pursue a career in singing, Hopkins found work as a backing singer for Bobby Wayne & the Dixies before forming her own band, Imagination. It was around this time that she changed her name to Sherene Davis, to avoid being confused with Welsh folk singer Mary Hopkin.

1975–1978: The World Starts Tonight and Natural Force
In 1975, Davis was spotted singing with her band in the Townsman Club, Swansea, by talent scout Roger Bell, who invited her to London to record a demo track. After many months had passed, she received a phone call from RCA Records, offering her a recording contract. They also recommended that she change her name again. After compiling a list of surnames and first names from a newspaper, Davis found a new name in "Bonnie Tyler".

Ronnie Scott and Steve Wolfe became her managers, songwriters and producers. "My! My! Honeycomb" was released as her debut single in April 1976, and failed to impact any charts worldwide. In September 1976, as part of a promotional campaign for Tyler's subsequent single release, "Lost in France", RCA Records allocated £4,000 for a strategic promotional initiative, which involved sending a group of 30 music journalists and radio DJs to Le Touquet, France, where they met Tyler over a four-course meal. "Lost in France" peaked at no. 9 in the UK and led to Tyler's first appearance on Top of the Pops. "More Than a Lover" followed in January 1977. Due to perceived sexual nature of the song's lyrics, it was banned from a new British children's TV series, Get It Together. Though surprised by the decision, Tyler stated she was grateful for the "extra publicity". It peaked at no. 27 in the UK.

Tyler's debut album, The World Starts Tonight, was released in February 1977. To promote the album, Tyler embarked on her first UK tour as a guest artist with Gene Pitney. The album failed to chart in the UK, but reached no. 2 in Sweden. In the spring of 1977, Tyler underwent an operation to remove vocal cord nodules and was advised by her doctor to rest her voice for six weeks. Tyler screamed in frustration one day, resulting in a permanent raspy tone.

In July 1977, Tyler released her fourth single, "Heaven". It peaked at no. 24 in Germany. Tyler ascribed the underwhelming performance of the single in other regions to the passing of Elvis Presley in August 1977. This event resulted in RCA redirecting its focus towards reissuing Presley's extensive back catalogue. "It's a Heartache" followed in November 1977 and became one of Tyler's most-successful singles, peaking at no. 4 in the UK and no. 3 on the Billboard Hot 100. "Here Am I" was released in April 1978, and it peaked at no. 4 in Norway. David Mackay parted ways with Ronnie Scott and Steve Wolfe in 1978, and Gordon Mills briefly took over as Tyler's manager. Mills organised Tyler's first tour of the United States in July 1978, including several nights at the Greek Theatre in Los Angeles, supporting Tom Jones.

Tyler's second studio album, Natural Force, was released in May 1978. It was certified Gold by the Recording Industry Association of America (RIAA), with sales of over half a million copies.

1979–1981: Diamond Cut and Goodbye to the Island
Ronnie Scott and Steve Wolfe produced Tyler's third album, Diamond Cut, with Robin Geoffrey Cable. Released in February 1979, it was a Top 20 record in Finland, Norway and Sweden, but only reached 145 in the US. Tyler felt that RCA was pushing her to record more country-oriented music, which frustrated her. The album yielded one major hit, "My Guns Are Loaded", which peaked at no. 10 on the Canadian AC chart.

In the summer of 1979, Tyler had another UK Top 40 hit with "(The World Is Full of) Married Men". She recorded it for a film adaptation of Jackie Collins' novel of the same name. Tyler performs the song during the film's closing titles.

In November 1979, Tyler represented the United Kingdom at the Yamaha World Popular Song Festival in Japan. She won the Grand Prix International award for her performance of "Sitting on the Edge of the Ocean", written by Ronnie Scott and Steve Wolfe. They co-produced Tyler's fourth album, Goodbye to the Island, with Hugh Murphy. Released in 1981, it only charted in Norway. RCA invited Tyler to extend her contract for another five years, but she declined, expressing disillusionment with her artistic image and noting a scarcity of performance opportunities in the aftermath of several unsuccessful singles.

1982–1989: The CBS Years
After her contract with RCA expired, Tyler signed with CBS/Columbia. A&R man Muff Winwood asked Tyler to scout a new producer. She considered Phil Collins, Jeff Lynne and Alan Tarney, but Jim Steinman was her first choice. "I'm a huge fan of his records, especially his solo album, and when my manager and I were discussing my comeback we both agreed that I had to sound the best or nobody would take me seriously." Steinman initially declined, but reconsidered after Tyler sent him demos of the rock material she was hoping to record.

After their initial meeting, Tyler returned to Steinman's apartment in New York a few weeks later where she performed "Total Eclipse of the Heart" with Rory Dodd. Steinman described the song as "a Wagnerian-like onslaught of sound and emotion", and a "showpiece" for Tyler's voice. Her fifth album was recorded at the Power Station in New York, with members of the E Street Band, Rick Derringer on guitar, Rory Dodd and Eric Troyer on backing vocals, and Steinman as producer.

"Total Eclipse of the Heart" was released in the UK on 11 February 1983. It became one of the best-selling singles of all time with over six million units sold. Her fifth studio album, Faster Than the Speed of Night, debuted at no. 1 on the UK Albums Chart and reached no. 3 on the US Cashbox chart and no. 4 on the US Billboard 200, selling over one million copies in the United States. Tyler's commercial success led to several award nominations, including two Grammys, two AMAs and a BRIT Award. Tyler was named Best Recording Artist at the Variety Club of Great Britain Awards, and she received a Goldene Europa.

Tyler also found success through some of her soundtrack recordings in the mid-80s. In 1984, she released "Holding Out for a Hero" from the Footloose soundtrack. In the following year, her recording of "Here She Comes" for Giorgio Moroder's restoration of the 1927 film Metropolis earned Tyler a Grammy nomination for Best Female Rock Vocal Performance. Tyler also declined an offer to record the theme for the James Bond spin-off Never Say Never Again.

In 1986, Tyler released her sixth studio album, Secret Dreams and Forbidden Fire. In another collaboration with Jim Steinman, the album also featured songs written by Desmond Child and Bryan Adams and a cover of "Band of Gold" by Freda Payne. "If You Were a Woman (And I Was a Man)" became the album's most successful single, selling over 250,000 units in France. The music video, directed by Steinman and Stuart Orme, received six nominations at the Billboard Video Music Conference.

In 1987, Tyler collaborated with Mike Oldfield on the title track to his album Islands. In the following year, Tyler played Polly Garter in George Martin's album Under Milk Wood, a radio drama by Dylan Thomas. The music was composed by Elton John, and features vocal contributions from Tom Jones, Anthony Hopkins and Mary Hopkin.

Tyler asked Desmond Child to produce her seventh album, Hide Your Heart, which came out on 9 May 1988. The album featured collaborations with Michael Bolton, Albert Hammond and Diane Warren. The album's singles, "Hide Your Heart", "Save Up All Your Tears" and "The Best" became major hits for other artists.

1990–2000: Success in continental Europe
In 1990, Tyler signed to Hansa/BMG Ariola and began working with various producers for her eighth studio album. She collaborated with Dieter Bohlen, Giorgio Moroder, Nik Kershaw and Roy Bittan. "We used so many producers in efforts to capture many different moods for many different territories, because we believed in the international crossover potential of Tyler," stated David Brunner, A&R manager for Hansa.

Bitterblue was released on 11 November 1991. In a retrospective review, AllMusic's Tomas Mureika noted that the album marked a "much more mainstream and less bombastic" direction in Tyler's career. The title track was released a month ahead of the album and became a top 40 hit in several European countries. It was named 'Catchy Song of the Year' at the RSH-Gold Awards. In the following year, "Bitterblue" was released as a promotional single in the United States where it was met with criticism. Billboard wrote that "bombastic production, with a rush of bagpipes and a choir of chirping children at the forefront, overpower Tyler's distinctive raspy voice."

While Bitterblue was never released in the UK or US, the album was a commercial success in mainland Europe. It topped the charts in Austria and Norway, achieving 4× Platinum status in the latter country with eleven weeks at no. 1.

Tyler's subsequent albums, Angel Heart (1992) and Silhouette in Red (1993), were also successful in mainland Europe. Both albums featured a greater share of songs written and produced by Dieter Bohlen. Tyler was named Best International Singer at the Goldene Europa Awards in 1993, and Best Pop/Rock Singer at the ECHO Awards in 1994.

In 1995, Tyler moved to EastWest Records and released Free Spirit. The album featured collaborations with a variety of producers including Humberto Gatica, David Foster and Jim Steinman. The lead single, a cover of Air Supply's "Making Love (Out of Nothing At All)", reached no. 45 on the UK Singles Chart in January 1996. The album was re-released in March 1996 featuring a cover of "Limelight" by the Alan Parsons Project. The track was used as a theme for the German team at the 1996 Summer Olympics in Atlanta, Georgia.

Tyler's twelfth studio album, All in One Voice, was released in 1998. Much of the album was recorded with Jimmy Smyth in Dublin, and Harold Faltermeyer in Hamburg.

In 1998, Tyler appeared on Rick Wakeman's orchestral album Return to the Centre of the Earth on the song "Is Anybody There?". The album also included narration from Star Trek actor Patrick Stewart and vocals from Ozzy Osbourne, Katrina Leskanich and Justin Hayward.

2001–2003: Greatest Hits and Heart Strings
On 14 September 2001, Tyler released Greatest Hits, a compilation album containing seventeen tracks. The album entered the UK Albums Chart at number 18, and was certified silver by the British Phonographic Industry (BPI) for sales of over 60,000 units. Greatest Hits reached the Top 10 in a further five European countries.

In 2002, Tyler began working on her thirteenth studio album, Heart Strings. EMI approached her with the idea of recording a cover album with an orchestra and Tyler's band. She selected thirteen songs by artists such as U2, The Beatles and Bruce Springsteen. The songs were arranged by composers Nick Ingman and Karl Jenkins, and performed by the City of Prague Philharmonic Orchestra.

Heart Strings was released on 18 March 2003, and was followed by a tour in Germany. The album charted in Europe, reaching the Top 50 in five countries.

2004–2005: Success in France
In 2003, vocalist Kareen Antonn invited Tyler to re-record "Total Eclipse of the Heart" as a bilingual duet in French and English. The new version was re-titled "Si demain... (Turn Around)" and released in December 2003. It went to no. 1 in Belgium and France, where it held the top position for ten weeks, selling over 500,000 units. The success of the single was considered to be Tyler's comeback in France, and received overwhelmingly positive reviews from music critics.

Tyler's fourteenth studio album Simply Believe was released in April 2004. It featured seven new songs and various re-recordings and covers. Tyler and Antonn recorded "Si tout s'arrête (It's a Heartache)" as a second bilingual duet. It peaked at number 12 in France. Tyler co-wrote the title track of the album, and two additional songs, with producer Jean Lahcene. Simply Believe spent 23 weeks on the French Album Charts and peaked at number 18.

Tyler released her fifteenth studio album Wings in the spring of 2005. It was recorded in Paris, and featured twelve new songs, two of which were also recorded in French, and new versions of "Total Eclipse of the Heart" and "It's a Heartache". Tyler promoted the album with an extensive tour of Europe, including a televised performance at the Sopot International Song Festival in Poland, and recorded concerts at La Cigale in Paris and at the Fiestas del Pilar in Zaragoza, Spain. Footage from all three concerts appeared on Tyler's live DVD Bonnie on Tour which was released in 2006. Wings was issued in the UK in 2006 under the title Celebrate. Tyler also received the Lifetime Achievement Steiger Award in 2005.

2006–2011: From the Heart: Greatest Hits and Best of 3 CD
In 2006, Tyler made her first appearance on US television in years when she performed "Total Eclipse of the Heart" with actress Lucy Lawless on Celebrity Duets. In the following year she recorded a new version of "Total Eclipse of the Heart" with punk band BabyPinkStar and released From the Heart: Greatest Hits, which reached number 2 in Ireland and number 31 in the UK.

In April 2009, Tyler joined Welsh male voice choir Only Men Aloud! on their UK tour to perform "Total Eclipse of the Heart". They recorded the song for their second studio album Band of Brothers, which was released in October. In the same year, she also recorded the title song for Mal Pope's new musical Cappuccino Girls, and performed the song at the opening night in Swansea's Grand Theatre. Tyler also made a cameo on Hollyoaks Later to sing "Holding Out for a Hero" in a dream sequence with Carmel McQueen (Gemma Merna).

In 2010, Tyler appeared in a television advertisement for MasterCard singing a parody of "Total Eclipse of the Heart". She released "Something Going On" with Country singer Wayne Warner and a new version of "Making Love (Out of Nothing At All)" with Matt Pétrin in July and August respectively. In October, she toured with Robin Gibb in Australia and New Zealand.

In 2011, Tyler appeared on Swedish TV show Kvällen är din ("The Evening Is Yours" in English), singing "Total Eclipse of the Heart" with Swedish singer Niklas Paulström. Tyler also performed "It's a Heartache". She also made a guest appearance in the music video "Newport (Ymerodraeth State of Mind)", a parody of the Jay-Z and Alicia Keys song "Empire State of Mind" for the BBC's Comic Relief charity. Also in 2011, Tyler won an award at the BMI London Awards for "It's a Heartache" gaining over three million airplays on US television and radio since it was first recorded in 1977. She also appeared on the Ukrainian version of X Factor as one of the three British guests, alongside Kylie Minogue and Cher Lloyd. She performed "It's a Heartache", "Total Eclipse of the Heart" and "Holding Out for a Hero". In December 2011, a portrait of Tyler by Rolf Harris, owned by Cathy Sims, was valued at £50,000 on BBC's Antiques Roadshow.

In September 2011, Tyler released a new compilation titled Best of 3 CD, which charted at number 36 in France. The album featured a cover of "Eternal Flame" by The Bangles, which was recorded as a duet with Laura Zen in French and English and released as a single.

2012–2018: Rocks and Honey and the Eurovision Song Contest
In early 2012, Tyler began working on her sixteenth album, Rocks and Honey. She travelled to Nashville, Tennessee in search of material for the album. It was recorded at the Blackbird Studios in Nashville, and produced by David Huff. Tyler sent the album to the BBC ahead of its release for feedback. After hearing the third track "Believe in Me", they asked Tyler to represent the United Kingdom with the song at the Eurovision Song Contest 2013. Although she was initially reluctant, Tyler accepted, describing Eurovision as "great publicity for my album".

Tyler was announced as the United Kingdom's entrant on 7 March 2013, and was met with a mixed reaction. "Believe in Me" was released on 13 March, and peaked at number 93 in the United Kingdom. As a member of the "Big Five", the United Kingdom automatically qualified to the Eurovision Grand Final on 18 May. Tyler finished in 19th place with 23 points. Reacting to the results, Tyler stated, "I did the best that I could do with a great song", adding, "I'm so glad and so happy that I did it because it was an incredible experience. It was like the Grammy awards all over again."

Following the Eurovision Song Contest, Tyler became the first representative for the United Kingdom to receive a Eurovision Song Contest Radio Award. She received the accolades for Best Song and Best Female Singer.

Rocks and Honey was released on 6 May 2013 in the United Kingdom, and peaked at number 52 on the UK Albums Chart. The album was titled in reference to the contrast between Tyler and Vince Gill's voice on their duet "What You Need from Me", which was likened to "rocks and honey". "This Is Gonna Hurt" and "Love Is the Knife" were released as the second and third singles in August and September 2013 respectively, though both songs failed to chart.

In 2014, Tyler released "Miserere" on Rhydian Roberts's album One Day like This, and "Fortune" on Spike's album 100% Pure Frankie Miller.

In June 2015, Tyler appeared on Die schönsten Disney Songs aller Zeiten, a one-off televised celebration of popular Disney songs in Germany. She performed "Circle of Life" from The Lion King. In September 2015, Tyler performed "Total Eclipse of the Heart" and "Holding Out for a Hero" on Best Time Ever with Neil Patrick Harris, Nicole Scherzinger and Alec Baldwin.

In 2016, Tyler featured on Frankie Miller's album Double Take. In March 2017, Tyler released a new single titled "Love's Holding On" with German metal band Axel Rudi Pell.

In August 2017, Tyler performed "Total Eclipse of the Heart" aboard the MS Oasis of the Seas with American dance-rock band DNCE to mark the solar eclipse of 21 August 2017. The song received an increase of 31,000 online downloads, which led to a placement of number 13 on the Billboard Digital Songs chart. In November, she released a new compilation titled Remixes and Rarities. The album debuted numerous tracks from her back catalogue that had not previously been released on CD.

In March 2018, Tyler embarked on a 22-date tour of Germany and Austria to celebrate the 40th anniversary of "It's a Heartache", with Sharron Levy as support.

2019–present: Recent albums
In February 2019, Tyler released "Hold On" as the lead single from her seventeenth studio album, Between the Earth and the Stars. The album followed in March 2019 and peaked at no. 34 on the UK Albums Chart. It was recorded with David Mackay, who produced Tyler's first two albums in the 1970s. Between the Earth and the Stars features three duets with Rod Stewart, Francis Rossi and Cliff Richard. Tyler embarked on a 23-date tour of Europe to support the album in April 2019, culminating with an appearance at BBC Proms in the Park in Hyde Park, London, and a headline concert at the London Palladium in September. Her show at L'Olympia in Paris was filmed and released through Canal+.

In August 2019, Cherry Red Records released a box set compiling Tyler's first four studio albums. Classic Pop magazine described The RCA Years as "a thoroughly-researched 4CD-set". In November 2019, Tyler made a guest appearance at Ben Zucker's concert at the Mercedes-Benz Arena, Berlin to sing "It's a Heartache". Their duet features on his live album, ''Wer Sagt das?! Zugabe!'', released in May 2020.

In December 2019, Tyler released a new version of her 2005 song "Streets of Stone" for The World's Big Sleep Out, an international homeless charity event. On 14 December 2019, she performed at the Vatican's annual Concerto di Natale in the presence of Pope Francis.

In May 2020, Tyler released "Through Thick and Thin (I'll Stand by You)" with Lorraine Crosby as a charity single in aid of the Teenage Cancer Trust. It reached no. 64 on the UK Downloads Chart. Her latest studio album, The Best Is Yet to Come, followed in February 2021.

On 2 September 2022, Tyler and Mike Batt released their duet "Into the Sunset" as a digital single. The track was originally released on the soundtrack to The Dreamstone in 1990. In October 2022, Tyler performed "Total Eclipse of the Heart" live with the cast of Tanz der Vampire in Stuttgart to mark the musical's 25th anniversary.

In November 2022, Tyler embarked on her first ever tour of South America, with eight dates in Brazil, and one date in Uruguay. Speaking with El País, Tyler stated that she hopes to release another studio album in 2023. Her memoir, Straight from the Heart, was published by Coronet Books on 28 September 2023.

On 19 April 2024, Tyler released her third live album, In Berlin. It was recorded at the Admiralspalast in Berlin during her Between the Earth and the Stars Live Tour on 8 May 2019. The album was preceded by its first single, "Faster Than the Speed of Night", on 22 March 2024.

Influences
Born into a musical family, Tyler grew up listening to a wide range of musical genres. One of Tyler's earliest musical memories was listening to her mother singing opera music in the family home. Tyler attended church until she was sixteen years old. Her first ever performance was singing "All Things Bright and Beautiful" in church. She was also exposed to the music of Elvis Presley, Frank Sinatra, The Beatles and other 1960s bands due to her siblings' musical tastes. Frankie Miller was the first live act that Tyler saw, and she later recorded duets with him.

Tyler's two biggest influences from a young age were Janis Joplin and Tina Turner. She cites "River Deep – Mountain High" as being her all-time favourite song. Other artists that influenced Tyler in her youth include Aretha Franklin, Wilson Pickett, Meat Loaf, Joe Cocker, Dusty Springfield and Tommy Steele. She has also expressed admiration for contemporary artists such as Guns N' Roses, Anastacia, Toni Braxton, Duffy, and Eminem. She has also expressed interest in collaborating with Adele, whom she describes as "a great song writer, singer and performer."

Vocal style
Tyler's music contains elements of country, rock, pop, blues and Celtic. Her voice has been likened to Rod Stewart and Kim Carnes as a result of her vocal cord nodule operation in the 1970s, sometimes even being referred to as "the female Rod Stewart", and, after her collaborations with Jim Steinman, "the female Meat Loaf". Soon after her operation, when recording her second album, Natural Force, the studio band complimented Tyler's changed voice. Reviewers from AllMusic have described Tyler's voice as "inimitable", "wonderfully gritty", and an "effective instrument" for drawing notice to her first managers, Ronnie Scott and Steve Wolfe.

In a review of Rocks and Honey, OMH Media described Tyler's vocals as being "good for only one thing and that's belting out gravelly vocals," suggesting that she sounds like Johnny Cash in his later years when she "tries to restrain [her voice]." With reference to her modern voice, The Yorkshire Times wrote that Tyler's vocals have "still got what it takes to make you tingle." Jim Steinman told People magazine that he wrote "Total Eclipse of the Heart" as a "showpiece for [Tyler's] voice." AllMusic said that Tyler's voice "produced the perfect type of 'desperate lovelorn' effect to suit the romantic lyrics."

Songwriting
Though songwriting has never been a significant part of Tyler's career, she has co-written a handful of B-Sides and other tracks. "Gonna Get Better", a B-Side to the 1980 Japanese single "Sayonara Tokyo", was written with her brother, Paul Hopkins.

In 2001, Tyler co-wrote four songs with Gary Pickford-Hopkins on his GPH album, and duetted with him on the track "Loving You Means Leaving You". Tyler was also involved in writing several tracks for her 2005 album Wings, including its singles "Louise" and "Celebrate".

Philanthropy
Tyler has featured in three charity supergroups. In 1986, she joined the Anti-Heroin Project to record "It's a Live-In World". The proceeds were donated to the Phoenix House Charities who funded heroin recovery centres in the UK. In the following year, Tyler featured as a chorus vocalist in the British-American charity group Ferry Aid, who released a cover of "Let It Be" by the Beatles. Proceeds were donated to a charity supporting the victims of the Zeebrugge Disaster. The single sold over 500,000 copies in the UK where it topped the charts for three weeks. In 1990, Tyler joined Rock Against Repatriation to record a cover of "Sailing". It was a protest song in response to the repatriation of Vietnamese boat people who fled to Hong Kong. The single peaked at no. 89 on the UK Singles Chart.

Since the 1990s, Tyler has been a patron of the Bobath Children's Therapy Centre in Cardiff, Wales, who provide care for children with cerebral palsy. In 2013, she campaigned for Bobath to be recognised at the Pride of Britain Awards. Tyler is also an ambassador for the Noah's Ark Children's Hospital for Wales. In January 2005, Tyler performed at the Rock for Asia benefit concert in Ingolstadt, Germany, raising funds for the victims of the 2004 Indian Ocean earthquake and tsunami. The event was recorded and released on DVD. In 2007, Tyler recorded "I Don't Know How to Love Him" for Over the Rainbow, a charity album conceptualised by Anneka Rice on the television show Challenge Anneka. The album reached no. 1 on the UK Compilation Chart, with proceeds going to the Association of Children's Hospices.

On 1 November 2009, Tyler performed as the headline act at the Pinktober Women in Rock concert at the Royal Albert Hall in London. In the following year, she co-headlined at a benefit concert alongside Leo Sayer raising funds for Variety, the Children's Charity, in New Zealand. In 2012, Tyler was named patron of the AAG animal charity association in Guia, Portugal. Tyler re-recorded "Holding Out for a Hero" for the 2013 Children in Need appeal. In 2014, she endorsed the BUAV's campaign to make it mandatory for animals in testing laboratories to be re-homed. In 2020, Tyler contributed to a cover of "Don't Answer Me" by the Alan Parsons Project to raise funds for Bergamo, an Italian city that was deeply impacted by the outbreak of the COVID-19 pandemic.

Personal life
In July 1973, Tyler married Robert Sullivan. He is a property developer and 1972 Olympic judo competitor. They have no children; Tyler miscarried when she was aged 39. Tyler and her family are Protestant.

Since 1988, Tyler and her husband have owned a five-bedroom home in Albufeira, Portugal in the Algarve. Tyler had recorded one of her albums there in the late 1970s, and the couple spend much of the year there. In 2005, Tyler was filmed in the Algarve for the Polish entertainment TV show Zacisze gwiazd, which explores the houses of actors and musicians.

Tyler and Sullivan have invested in property. As of a 1999 interview, they owned farmland in Portugal and New Zealand, 22 houses in Berkshire and London, and 65 stables offering horse boarding services. In a 2013 interview, Tyler stated that the farm in New Zealand had been converted to a dairy farm twelve years after they purchased the land. In the same interview, she stated that she and Sullivan also own a quarry.

Studio albums

 * The World Starts Tonight (1977)
 * Natural Force (1978)
 * Diamond Cut (1979)
 * Goodbye to the Island (1981)
 * Faster Than the Speed of Night (1983)
 * Secret Dreams and Forbidden Fire (1986)
 * Hide Your Heart (1988) also known as Notes From America
 * Bitterblue (1991)
 * Angel Heart (1992)
 * Silhouette in Red (1993)
 * Free Spirit (1995)
 * All in One Voice (1998)
 * Heart Strings (2003) also known as Heart & Soul
 * Simply Believe (2004)
 * Wings (2005) also known as Celebrate
 * Rocks and Honey (2013)
 * Between the Earth and the Stars (2019)
 * The Best Is Yet to Come (2021)

Honours, awards and recognition
"Total Eclipse of the Heart" and "It's a Heartache" have estimated sales of over 6 million units each, and are among the best-selling singles of all time.

Tyler's 1976 breakthrough with "Lost in France" led to her nomination for Best British Female Newcomer at the 1977 Brit Awards. In the 1980s, she received nominations for two more Brit Awards, and three Grammy Awards. In 2013, she was presented with the Gold Badge award by the British Academy of Songwriters, Composers and Authors (BASCA).

In 1979, Tyler won the 10th World Popular Song Festival with "Sitting on the Edge of the Ocean", representing the United Kingdom. Tyler also became the first and only representative of the United Kingdom to receive a Eurovision Song Contest Radio award in 2013. She was also one of the first western artists to tour the Soviet Union.

In addition to her music awards, Tyler has received local honours in Wales; including being named freeman of Neath Port Talbot in 2011, and an honorary degree and doctorate from Swansea University in 2013. She is also an Honorary Fellow of the Royal Welsh College of Music & Drama. In 2016, she was honoured by the Lord Mayor of Swansea for Services to Music.

Tyler was appointed Member of the Order of the British Empire (MBE) in the 2022 Birthday Honours for services to music.

title: Bonnie Tyler


text:
Path

A path is a route for physical travel – see Trail.

Path or PATH may also refer to:

Physical paths of different types

 * Bicycle path
 * Bridle path, used by people on horseback
 * Course (navigation), the intended path of a vehicle
 * Desire path, created by human or animal foot traffic
 * Footpath, intended for use only by pedestrians
 * Shared-use path, intended for multiple modes such as walking, bicycling, in-line skating or others
 * Sidewalk, a paved path along the side of a road
 * Hoggin, a buff-coloured gravel & clay pathway often seen in gardens of Stately Homes, Parks etc.

 * Trail, an unpaved lane or road

Mathematics, physics, and computing

 * Path (computing), in file systems, the human-readable address of a resource
 * PATH (variable), in computing, a way to specify a list of directories containing executable programs
 * Path (graph theory), a sequence of edges of a graph that form a trail
 * st-connectivity problem, sometimes known as the "path problem"
 * Path (topology), a continuous function
 * Path (geometry), a curve
 * Path, a name for the vectors in vector graphics
 * Clipping path, in digital image processing
 * Path (physics), a trajectory

Organizations

 * PATH (global health organization), an international nonprofit organization in Seattle
 * Partners for Advanced Transit and Highways, a research organization operated by the University of California
 * PATH Foundation, a trail-building organization in Georgia, USA
 * People's Alliance of Tower Hamlets, a minor political party in Tower Hamlets, London
 * Positive Alternatives to Homosexuality, a coalition of anti-gay organizations
 * Professional Association of Therapeutic Horsemanship, a non-profit organization that promotes the benefits equine-assisted therapies
 * Projects for Assistance in Transition from Homelessness, American formula grant program

Other uses

 * Path (social network), a photo sharing and messaging service
 * PATH (rail system), Port Authority Trans-Hudson, serving New York and New Jersey
 * Path (Toronto), a network of underground pedestrian tunnels in Toronto, Ontario, Canada
 * Golden Path (Dune), a metaphysical theme from Frank Herbert's Dune novels
 * "Path Vol. 1 & 2", a 2000 single by Apocalyptica
 * Potomac-Appalachian Transmission Highline, a proposed electrical line
 * Train path, infrastructure capacity needed to run a train between two places over a given time-period
 * Path (album), by American shoegaze musician Kraus

title: Path


text:
Talk:August Ferdinand Möbius

Initial remarks
Dear Vicki What exactlly did you mean with your tag [copyedit (what's with all these one-sentence entries on mathematicians?)]. Is there anything and what wrong with "one-sentence" entries on mathematicians. Do you mean such sentences where there are just data of birth and death or something elese? I am curious to know. I've put there-in just for futher developments some of the most important SLovene mathematicians and I do hope that do not bothers you. Geet my best regards from Slovenia. XJamRastafire 3 Wednesday [2002.02.27]

Generally, I usually differ to Vicki's jundgement -- she is a professional copyediter. However, in this case I think her statement was out of place. The entries I saw where good definition entries of mathematicians that really should be in any respectable encylopedia. Many of these will now develop into good articles -- and those that don't will remain definitions. The same is true for hardcover encyclopedias -- sometimes there just isn't enough interest in a particular person to write more than a good definition entry. Just my 2 cents. maveric149

Although both spellings (Möbius and Moebius) are acceptable (they didn't have strict spellings back in the 18th century), I think we should standardise on one of them for the title of articles such as Moebius strip/Moebius function vs. Möbius inversion formula. So I'll start a vote here... -- Timwi 23:05 24 Jun 2003 (UTC)
 * Möbius: (2) Timwi Revolver
 * Moebius: (0)

I'm a little confused by the notion of "posthumous co-discovery". Perhaps someone could explain scientific work from beyond the grave? -- VV 08:16, 31 Oct 2003 (UTC)

 * I'm not sure...TBOMK, it was co-discovered in 1858, long before Mobius took his final breath. Revolver 10 Nov 2003

What about a picture
In think this article could use a good picture of August Möbius, wich im sure could be found anywhere, rather than only of his Möbius strip. The reason I dont do it it's because i'm not sure how.--64.32.92.84 23:33, 4 May 2007 (UTC)

Date of birth
Why are there two different dates of birth in one article? I don't know his real birthday, but only one of them can be right! Erwin 13:57, 8 May 2007 (UTC)

First names
An i.p. editor (claiming irrelevantly to be a descendant) changed Herr Möbius's first name in the Möbius strip article from August to Augustus. I have reverted because (1) it should match the spelling in this article and (2) a majority of reliable sources I checked say it's August. However, it may be worth noting that the Columbia Encyclopedia says it's Augustus. That may be an error, but the Google hits are just about equal for both forms and not all of the –us hits are junk, by any means. I thought I'd bring this up here, in case anyone eventually wanders by who can shed any light. Rivertorch (talk) 07:35, 7 March 2009 (UTC)

Assessment comment
Substituted at 08:35, 29 April 2016 (UTC)

title: Talk:August Ferdinand Möbius


text:
Mass noun

In linguistics, a mass noun, uncountable noun, non-count noun, uncount noun, or just uncountable, is a noun with the syntactic property that any quantity of it is treated as an undifferentiated unit, rather than as something with discrete elements. Uncountable nouns are distinguished from count nouns.

Given that different languages have different grammatical features, the actual test for which nouns are mass nouns may vary between languages. In English, mass nouns are characterized by the impossibility of being directly modified by a numeral without specifying a unit of measurement and by the impossibility of being combined with an indefinite article (a or an). Thus, the mass noun "water" is quantified as "20 litres of water" while the count noun "chair" is quantified as "20 chairs". However, both mass and count nouns can be quantified in relative terms without unit specification (e.g., "so much water", "so many chairs", though note the different quantifiers "much" and "many").

Mass nouns have no concept of singular and plural, although in English they take singular verb forms. However, many mass nouns in English can be converted to count nouns, which can then be used in the plural to denote (for instance) more than one instance or variety of a certain sort of entity – for example, "Many cleaning agents today are technically not soaps [i.e. types of soap], but detergents," or "I drank about three beers [i.e. bottles or glasses of beer]".

Some nouns can be used indifferently as mass or count nouns, e.g., three cabbages or three heads of cabbage; three ropes or three lengths of rope. Some have different senses as mass and count nouns: paper is a mass noun as a material (three reams of paper, one sheet of paper), but a count noun as a unit of writing ("the students passed in their papers").

Grammatical number and physical discreteness
In English (and in many other languages), there is a tendency for nouns referring to liquids (water, juice), powders (sugar, sand), or substances (metal, wood) to be used in mass syntax, and for nouns referring to objects or people to be count nouns. But there are many exceptions: the mass/count distinction is a property of the terms, not their referents. For example, the same set of chairs can be referred to as "seven chairs" (count) and as "furniture" (mass); the Middle English mass noun pease has become the count noun pea by morphological reanalysis; "vegetables" are a plural count form, while the British English slang synonym "veg" is a mass noun.

In languages that have a partitive case, the distinction is explicit and mandatory. For example, in Finnish, join vettä, "I drank (some) water", the word vesi, "water", is in the partitive case. The related sentence join veden, "I drank (the) water", using the accusative case instead, assumes that there was a specific countable portion of water that was completely drunk.

The work of logicians like Godehard Link and Manfred Krifka established that the mass/count distinction can be given a precise, mathematical definition in terms of quantization and cumulativity.

Cumulativity and mass nouns
An expression P has cumulative reference if and only if for any X and Y: In more formal terms (Krifka 1998):
 * If X can be described as P and Y can be described as P, as well, then the sum of X and Y can also be described as P.

 * $$\forall X \subseteq U_p [\mathrm{CUM}_p (X) \Leftrightarrow \exists x,y [ X(x) \,\wedge\, X(y) \,\wedge\, \neg (x=y)] \;\wedge\; \forall x,y [X(x) \,\wedge\, X(y) \Rightarrow X(x \,\oplus\, y)]]$$

which may be read as: X is cumulative if there exists at least one pair x,y, where x and y are distinct, and both have the property X, and if for all possible pairs x and y fitting that description, X is a property of the sum of x and y.

Consider, for example cutlery: If one collection of cutlery is combined with another, we still have "cutlery." Similarly, if water is added to water, we still have "water." But if a chair is added to another, we do not have "a chair", but rather two chairs. Thus the nouns "cutlery" and "water" have cumulative reference, while the expression "a chair" does not. The expression "chairs", however, does, suggesting that the generalization is not actually specific to the mass-count distinction. As many have noted, it is possible to provide an alternative analysis, by which mass nouns and plural count nouns are assigned a similar semantics, as distinct from that of singular count nouns.

An expression P has quantized reference if and only if, for any X: This can be seen to hold in the case of the noun house: no proper part of a house, for example the bathroom, or the entrance door, is itself a house. Similarly, no proper part of a man, say his index finger, or his knee, can be described as a man. Hence, house and man have quantized reference. However, collections of cutlery do have proper parts that can themselves be described as cutlery. Hence cutlery does not have quantized reference. Notice again that this is probably not a fact about mass-count syntax, but about prototypical examples, since many singular count nouns have referents whose proper parts can be described by the same term. Examples include divisible count nouns like "rope", "string", "stone", "tile", etc.
 * If X can be described as P, then no proper part of X can be described as P.

Some expressions are neither quantized nor cumulative. Examples of this include collective nouns like committee. A committee may well contain a proper part which is itself a committee. Hence this expression is not quantized. It is not cumulative, either: the sum of two separate committees is not necessarily a committee. In terms of the mass/count distinction, committee behaves like a count noun. By some accounts, these examples are taken to indicate that the best characterization of mass nouns is that they are cumulative nouns. On such accounts, count nouns should then be characterized as non-cumulative nouns: this characterization correctly groups committee together with the count nouns. If, instead, we had chosen to characterize count nouns as quantized nouns, and mass nouns as non-quantized ones, then we would (incorrectly) be led to expect committee to be a mass noun. However, as noted above, such a characterization fails to explain many central phenomena of the mass-count distinction.

Multiple senses for one noun
Many English nouns can be used in either mass or count syntax, and in these cases, they take on cumulative reference when used as mass nouns. For example, one may say that "there's apple in this sauce", and then apple has cumulative reference, and, hence, is used as a mass noun. The names of animals, such as "chicken", "fox" or "lamb" are count when referring to the animals themselves, but are mass when referring to their meat, fur, or other substances produced by them. (e.g., "I'm cooking chicken tonight" or "This coat is made of fox.") Conversely, "fire" is frequently used as a mass noun, but "a fire" refers to a discrete entity. Substance terms like "water" which are frequently used as mass nouns, can be used as count nouns to denote arbitrary units of a substance ("Two waters, please") or of several types/varieties ("waters of the world"). One may say that mass nouns that are used as count nouns are "countified" and that count ones that are used as mass nouns are "massified". However, this may confuse syntax and semantics, by presupposing that words which denote substances are mass nouns by default. According to many accounts, nouns do not have a lexical specification for mass-count status, and instead are specified as such only when used in a sentence. Nouns differ in the extent to which they can be used flexibly, depending largely on their meanings and the context of use. For example, the count noun "house" is difficult to use as mass (though clearly possible), and the mass noun "cutlery" is most frequently used as mass, despite the fact that it denotes objects, and has count equivalents in other languages:

 * Incorrect: *There is house on the road. (Incorrect even if a catastrophe is considered)
 * Incorrect: *There is a cutlery on the table. (Incorrect even if just one fork is on the table)
 * Correct: You got a lot of house for your money since the recession.
 * Correct: Spanish cutlery is my favorite. (type / kind reading)

In some languages, such as Chinese and Japanese, it has been claimed by some that all nouns are effectively mass nouns, requiring a measure word to be quantified.

Quantification
Some quantifiers are specific to mass nouns (e.g., an amount of) or count nouns (e.g., a number of, every). Others can be used with both types (e.g., a lot of, some).

Words fewer and less
Where much and little qualify mass nouns, many and few have an analogous function for count nouns:
 * How much damage? —Very little.
 * How many mistakes? —Very few.

Whereas more and most are the comparative and superlative of both much and many, few and little have differing comparative and superlative (fewer, fewest and less, least). However, suppletive use of less and least with count nouns is common in many contexts, some of which attract criticism as nonstandard or low-prestige. This criticism dates back to at least 1770; the usage dates back to Old English. In 2008, Tesco changed supermarket checkout signs reading "Ten items or less" after complaints that it was bad grammar; at the suggestion of the Plain English Campaign it switched to "Up to ten items" rather than to "Ten items or fewer".

Conflation of collective noun and mass noun
There is often confusion about the two different concepts of collective noun and mass noun. Generally, collective nouns such as group, family, and committee are not mass nouns but are rather a special subset of count nouns. However, the term "collective noun" is often used to mean "mass noun" (even in some dictionaries) because users conflate two different kinds of verb number invariability: (a) that seen with mass nouns such as "water" or "furniture", with which only singular verb forms are used because the constituent matter is grammatically indivisible (although it may ["water"] or may not ["furniture"] be etically indivisible); and (b) that seen with collective nouns, which is the result of the metonymical shift between the group and its (both grammatically and etically) discrete constituents.

Some words, including "mathematics" and "physics", have developed true mass-noun senses despite having grown from count-noun roots.

title: Mass noun