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Category Archives: Inspiration-O-Matic
France is not just famous for its wine but also for its medival towns and other sights. We stayed in the Alsace, which switched between being German and French territory in the past. That is why it is not mandatory to speak French; you can also get along speaking German or English. Enjoying the beautiful weather, we could wander a couple of well-preserved medival towns like Munster, Eguisheim, Requewihr and Colmar.
Eguisheim is a good example of the structure of a medival city: as you can see on the picture below, a circular road encompasses the inner city, in which you can find a small castle and the St.-Leo Chapel. (For those interested in history: Leo is the pope who introduced celibacy.) What’s also beautiful, is that you can see the remains of the old city walls in the back of the houses on the left hand side. In Requewihr, you can also find well-preserved houses, but the city is crowded with tourists and the houses are painted in bright colours (it reminds me of Disneyland).
We did not just pass out time by wandering medieval cities, but we also went to see a castle: Haut-Koenigsburg (German: Hohenkönigsburg; see picture below). There you could get an idea of how few space there is in a castle: even the chamber of the empress just measured 215 sqare feet and the widest hall maybe 750. What you could also see, were diffent kinds of weaponry and armaments.
To put it in a nutshell – nice weather – great wine – delicious food – interesting places – awesome!
The game won’t be finished soon, but the development of a storyline is a long process, which passes several steps. With my background it immediately suggests itself to see the story-writing-process as a kind of literary-art-project (like it is planned and performed in the school subject “literature” in North Rhine-Westphalia). These kinds of projects pass five different stages: 1. getting started; 2. finding a topic; 3. developing the topic; 4. writing; 5. text-revision. This entry is just about the first stage: getting started. (As you can guess from the “(1)” in the headline, there will be more entries concerning this topic )
Since the secretary problem in its standard form did not meet our requirements, I want to take a first glimpse at extensions seen in the literature. We already mentioned four points of criticism, let’s have a look at related extensions:
The objective value in the standard form of the secretary problem is either 1 (best candidate was chosen) or 0 (otherwise). In our case the objective value is the utility of the chosen candidate aka offer (minus evaluation costs). General utility functions for the secretary problem have already been introduces in 1973 by Mucci. The thus modified problem is (considering some additional requirements that are satisfied) solvable .
In the standard version the candidates visit the decision maker, the NPC will lateron have to travel to the next merchant. This causes evaluation costs (the travel time). Evaluation costs have been dealt with in the literature, first one to do so war Lorenzen in 1978 . There is (under certain circumstances) a closed form solution for this modified problem, even regarding general utility functions .
A once rejected problem is (in the standard form of the secretary problem) lost forever. The NPC will be able to revisit the merchant of a rejected offer and accept the already rejected offer (if it is still available). This extension was first introduced in 1974 by Yang , it can be solved using dynamic programming .
Also our last item – an unknown number of candidates – was already considered in literature. But this item can be handled without further thoughts – it can be easily seen that due to the evaluation costs the number of merchants that we will see is limited.
So far with our item-by-item consideration.. But we need all extension at the same time.. So let’s see how well thay can be combined..
 P.R. Freeman. (1983). The Secretary Problem and its Extensions: A Review. International Statistical Review, 51 (1983), pp. 189-206.
 Smith, M.H. (1975). A secretary problem with uncertain employment. J. Appl. Prob. 12, pp. 620-624.
 Mucci, A.G. (1973). Differential equations and optimal choice problems. Ann. Statist. 1, pp. 104-113.
 Lorenzen, T. J. (1978). Generalising the secretary problem. Adv. Appl. Prob. 11, pp. 384-396.
 Lorenzen, T. J. (1981). Optimal stopping with sampling cost: the secretary problem. Ann. Prob. 9, pp. 167-172.
The NPC can now not only calculate the fair price using time series analysis, he can also determine the offer’s expected utilitys as the difference of the good’s and the money’s utility (see also Money and Utility). But how does he decide whether to accept the offer or decline the offer in the hope of finding a better offer? A first step towards the answer could be the secretary problem, whose standard form I want to introduce in this article.
In the standard form of the secretary problem n candidates audition for a job and after the evaluation of the current applicant he or she is immediately accepted or rejected for the job. Exactly one applicant has to be accepted (meaning once an applicant is accepted, all other (maybe better) applicants are automatically rejected) and all applicants that are rejected are lost for sure. There are only two possible results: win (the best applicant was chosen, so the objective value is 1) or loose (the best applicant was not chosen, the objective value is 0). The task is finding an optimal acceptance / denial strategy that maximizes the chance of winning. 
In this plain vanilla version the secretary can be solved fairly easily . But the NPC’s situation is not captured, for example:
- The objective value is the utility of the accepted offer (minus the evaluation costs) and is not set to zero just because there would have been a better option.
- The evaluation of options costs time.
- It is possible to revisit an already evaluated option, this again costs evaluation costs and may eventually turn out not to be available any more.
- The number of offers may not necessarily be known in advance.
 P.R. Freeman. 1983. The Secretary Problem and its Extensions: A Review. International Statistical Review, 51 (1983), pp. 189-206.
Another great material for accessoires and clothing surely are borrowed feathers. From well-known, netive species to exotic and rare birds – their feathers do suit us The more outstanding, more rare, harder to get the higher will probably be their price. And thy can be useful, too – for example as a feather fill.