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'''Bayesian search theory''' is the application of [[Bayesian statistics]] to the search for lost objects. It has been used several times to find lost sea vessels, for example the [[USS Scorpion (SSN-589)|USS ''Scorpion'']]. It also played a key role in the recovery of the flight recorders in the [[Air France Flight 447]] disaster of 2009.
It is very common to have a dental emergency -- a fractured tooth, an abscess, or severe pain when chewing. Over-the-counter pain medication is just masking the problem. Seeing an emergency dentist is critical to getting the source of the problem diagnosed and corrected as soon as possible.<br><br><br><br>Here are some common dental emergencies:<br>Toothache: The most common dental emergency. This generally means a badly decayed tooth. As the pain affects the tooth's nerve, treatment involves gently removing any debris lodged in the cavity being careful not to poke deep as this will cause severe pain if the nerve is touched. Next rinse vigorously with warm water. Then soak a small piece of cotton in oil of cloves and insert it in the cavity. This will give temporary relief until a dentist can be reached.<br><br>At times the pain may have a more obscure location such as decay under an old filling. As this can be only corrected by a dentist there are two things you can do to help the pain. Administer a pain pill (aspirin or some other analgesic) internally or dissolve a tablet in a half glass (4 oz) of warm water holding it in the mouth for several minutes before spitting it out. DO NOT PLACE A WHOLE TABLET OR ANY PART OF IT IN THE TOOTH OR AGAINST THE SOFT GUM TISSUE AS IT WILL RESULT IN A NASTY BURN.<br><br>Swollen Jaw: This may be caused by several conditions the most probable being an abscessed tooth. In any case the treatment should be to reduce pain and swelling. An ice pack held on the outside of the jaw, (ten minutes on and ten minutes off) will take care of both. If this does not control the pain, an analgesic tablet can be given every four hours.<br><br>Other Oral Injuries: Broken teeth, cut lips, bitten tongue or lips if severe means a trip to a dentist as soon as possible. In the mean time rinse the mouth with warm water and place cold compression the face opposite the injury. If there is a lot of bleeding, apply direct pressure to the bleeding area. If bleeding does not stop get patient to the emergency room of a hospital as stitches may be necessary.<br><br>Prolonged Bleeding Following Extraction: Place a gauze pad or better still a moistened tea bag over the socket and have the patient bite down gently on it for 30 to 45 minutes. The tannic acid in the tea seeps into the tissues and often helps stop the bleeding. If bleeding continues after two hours, call the dentist or take patient to the emergency room of the nearest hospital.<br><br>Broken Jaw: If you suspect the patient's jaw is broken, bring the upper and lower teeth together. Put a necktie, handkerchief or towel under the chin, tying it over the head to immobilize the jaw until you can get the patient to a dentist or the emergency room of a hospital.<br><br>Painful Erupting Tooth: In young children teething pain can come from a loose baby tooth or from an erupting permanent tooth. Some relief can be given by crushing a little ice and wrapping it in gauze or a clean piece of cloth and putting it directly on the tooth or gum tissue where it hurts. The numbing effect of the cold, along with an appropriate dose of aspirin, usually provides temporary relief.<br><br>In young adults, an erupting 3rd molar (Wisdom tooth), especially if it is impacted, can cause the jaw to swell and be quite painful. Often the gum around the tooth will show signs of infection. Temporary relief can be had by giving aspirin or some other painkiller and by dissolving an aspirin in half a glass of warm water and holding this solution in the mouth over the sore gum. AGAIN DO NOT PLACE A TABLET DIRECTLY OVER THE GUM OR CHEEK OR USE THE ASPIRIN SOLUTION ANY STRONGER THAN RECOMMENDED TO PREVENT BURNING THE TISSUE. The swelling of the jaw can be reduced by using an ice pack on the outside of the face at intervals of ten minutes on and ten minutes off.<br><br>If you have any concerns relating to where by and how to use [http://www.youtube.com/watch?v=90z1mmiwNS8 Washington DC Dentist], you can call us at our own web-site.
 
==Procedure==
 
The usual procedure is as follows:
 
# Formulate as many reasonable hypotheses as possible about what may have happened to the object.  
# For each hypothesis, construct a [[probability density function]] for the location of the object.
# Construct a function giving the probability of actually finding an object in location&nbsp;X when searching there if it really is in location&nbsp;X. In an ocean search, this is usually a function of water depth — in shallow water chances of finding an object are good if the search is in the right place. In deep water chances are reduced.
# Combine the above information coherently to produce an overall probability density map. (Usually this simply means multiplying the two functions together.) This gives the probability of finding the object by looking in location&nbsp;X, for all possible locations&nbsp;X. (This can be visualized as a [[contour map]] of probability.)
# Construct a search path which starts at the point of highest probability and 'scans' over high probability areas, then intermediate probabilities, and finally low probability areas.
# Revise all the probabilities continuously during the search. For example, if the hypotheses for location&nbsp;X imply the likely disintegration of the object and the search at location&nbsp;X has yielded no fragments, then the probability that the object is somewhere around there is greatly reduced (though not usually to zero) while the probabilities of its being at other locations is correspondingly increased. The revision process is done by applying [[Bayes' theorem]].
 
In other words, first search where it most probably will be found, then search where finding it is less probable, then search where the probability is even less (but still possible due to limitations on fuel, range, water currents, etc.), until insufficient hope of locating the object at acceptable cost remains.
 
The advantages of the Bayesian method are that all information available is used coherently (i.e., in a "leak-proof" manner) and the method automatically produces estimates of the cost for a given success probability. That is, even before the start of searching, one can say, hypothetically, "there is a 65% chance of finding it in a 5-day search. That probability will rise to 90% after a 10-day search and 97% after 15&nbsp;days" or a similar statement. Thus the economic viability of the search can be estimated before committing resources to a search.
 
Apart from the [[USS Scorpion (SSN-589)|USS ''Scorpion'']], other vessels located by Bayesian search theory include the [[MV Derbyshire|MV&nbsp;''Derbyshire'']], the largest British vessel ever lost at sea, and the [[SS Central America|SS&nbsp;''Central America'']]. It also proved successful in the search for a lost [[hydrogen bomb]] following the [[1966 Palomares B-52 crash]] in Spain, and the recovery in the Atlantic Ocean of the crashed [[Air France Flight 447]].
 
Bayesian search theory is incorporated into the CASP (Computer Assisted Search Program) mission planning software used by the [[United States Coast Guard]] for [[search and rescue]]. This program was later adapted for inland search by adding terrain and ground cover factors for use by the [[United States Air Force]] and [[Civil Air Patrol]].
 
==Mathematics==
 
Suppose a grid square has a probability ''p'' of containing the wreck and that the probability of successfully detecting the wreck if it is there is ''q''. If the square is searched and no wreck is found, then, by Bayes' theorem, the revised probability of the wreck being in the square is given by
 
: <math> p' = \frac{p(1-q)}{(1-p)+p(1-q)} = p \frac{1-q}{1-pq} < p.</math>
For each other grid square, if its prior probability is ''r'', its posterior probability is given by
 
: <math> r' = r \frac{1}{1- pq} > r. </math>
 
 
==Optimal Distribution of Search Effort==
 
The classical book on this subject, based on probabilistic information, by [[Lawrence D. Stone]] won the 1975 [[Frederick W. Lanchester Prize]] by the [[Operations Research Society of America]].
 
 
 
<!-- Material on USS Scorpion, moved from Bayesian inference
 
In May 1968, the [[U.S. Navy]]'s [[nuclear submarine]] [[USS Scorpion (SSN-589)|USS ''Scorpion'' (SSN-589)]] failed to arrive as expected at her home port of [[Norfolk, Virginia]]. The command officers of the U.S. Navy were nearly convinced that the vessel had been lost off the [[East Coast of the United States|Eastern Seaboard]],  but an extensive search there failed to discover the remains of the ''Scorpion''.
 
Then, a Navy deep-water expert, [[John Craven USN|John P. Craven]], suggested that the USS ''Scorpion'' had sunk elsewhere. Craven organised a search southwest of the [[Azores]] based on a controversial approximate triangulation by [[hydrophone]]s. He was allocated only a single ship, the [[USNS Mizar (AGOR-11)|''Mizar'']], and he took advice from a firm of consultant mathematicians in order to maximise his resources. A Bayesian search methodology was adopted. Experienced submarine commanders were interviewed to construct hypotheses about what could have caused the loss of the ''Scorpion''.
 
The sea area was divided up into grid squares and a probability assigned to each square, under each of the hypotheses, to give a number of probability grids, one for each hypothesis. These were then added together to produce an overall probability grid. The probability attached to each square was then the probability that the wreck was in that square. A second grid was constructed with probabilities that represented the probability of successfully finding the wreck if that square were to be searched and the wreck were to be actually there. This was a known function of water depth. The result of combining this grid with the previous grid is a grid which gives the probability of finding the wreck in each grid square of the sea if it were to be searched.
 
 
==Optimal Distribution of Search Effort==
 
The classical book on this subject by [[Lawrence D. Stone]] won the 1975 [[Lancaster Prize]] by the American Operations Research Society.
 
-->
 
==See also==
* [[Bayesian inference]]
* [[Search games]]
 
== References ==
* [[Stone, Lawrence D.]], ''The Theory of Optimal Search'', published by the [[Operations Research Society of America]], 1975
* [[Stone, Lawrence D.]], In search of Air France Flight 447. Institute of Operations Research and the Management Sciences, 2011
* Iida, Koji., '' Studies on the Optimal Search Plan'', Vol.&nbsp;70, Lecture Notes in Statistics, Springer-Verlag, 1992.
* De Groot, Morris H., ''Optimal Statistical Decisions'', Wiley Classics Library, 2004.
* Richardson, Henry R; and Stone, Lawrence D. Operations Analysis during the underwater search for ''Scorpion''. ''Naval Research Logistics Quarterly'', June&nbsp;1971, Vol.&nbsp;18, Number&nbsp;2. Office of Naval Research.
* Stone, Lawrence D. Search for the SS ''Central America'': Mathematical Treasure Hunting. Technical Report, Metron Inc. Reston, Virginia.
* [[Bernard Koopman|Koopman, B.O.]] ''Search and Screening'', Operations Research Evaluation Group Report 56, Center for Naval Analyses, Alexandria, Virginia. 1946.
* Richardson, Henry R; and Discenza, J.H. The United States Coast Guard computer-assisted search planning system (CASP). ''Naval Research Logistics Quarterly''. Vol.&nbsp;27 number&nbsp;4. pp.&nbsp;659–680. 1980.
* [[Ross, Sheldon M.]], ''An Introduction to Stochastic Dynamic Programming'', Academic Press. 1983.
 
[[Category:Bayesian statistics|Search theory]]
[[Category:Searching]]
[[Category:Operations research]]

Revision as of 05:22, 26 February 2014

It is very common to have a dental emergency -- a fractured tooth, an abscess, or severe pain when chewing. Over-the-counter pain medication is just masking the problem. Seeing an emergency dentist is critical to getting the source of the problem diagnosed and corrected as soon as possible.



Here are some common dental emergencies:
Toothache: The most common dental emergency. This generally means a badly decayed tooth. As the pain affects the tooth's nerve, treatment involves gently removing any debris lodged in the cavity being careful not to poke deep as this will cause severe pain if the nerve is touched. Next rinse vigorously with warm water. Then soak a small piece of cotton in oil of cloves and insert it in the cavity. This will give temporary relief until a dentist can be reached.

At times the pain may have a more obscure location such as decay under an old filling. As this can be only corrected by a dentist there are two things you can do to help the pain. Administer a pain pill (aspirin or some other analgesic) internally or dissolve a tablet in a half glass (4 oz) of warm water holding it in the mouth for several minutes before spitting it out. DO NOT PLACE A WHOLE TABLET OR ANY PART OF IT IN THE TOOTH OR AGAINST THE SOFT GUM TISSUE AS IT WILL RESULT IN A NASTY BURN.

Swollen Jaw: This may be caused by several conditions the most probable being an abscessed tooth. In any case the treatment should be to reduce pain and swelling. An ice pack held on the outside of the jaw, (ten minutes on and ten minutes off) will take care of both. If this does not control the pain, an analgesic tablet can be given every four hours.

Other Oral Injuries: Broken teeth, cut lips, bitten tongue or lips if severe means a trip to a dentist as soon as possible. In the mean time rinse the mouth with warm water and place cold compression the face opposite the injury. If there is a lot of bleeding, apply direct pressure to the bleeding area. If bleeding does not stop get patient to the emergency room of a hospital as stitches may be necessary.

Prolonged Bleeding Following Extraction: Place a gauze pad or better still a moistened tea bag over the socket and have the patient bite down gently on it for 30 to 45 minutes. The tannic acid in the tea seeps into the tissues and often helps stop the bleeding. If bleeding continues after two hours, call the dentist or take patient to the emergency room of the nearest hospital.

Broken Jaw: If you suspect the patient's jaw is broken, bring the upper and lower teeth together. Put a necktie, handkerchief or towel under the chin, tying it over the head to immobilize the jaw until you can get the patient to a dentist or the emergency room of a hospital.

Painful Erupting Tooth: In young children teething pain can come from a loose baby tooth or from an erupting permanent tooth. Some relief can be given by crushing a little ice and wrapping it in gauze or a clean piece of cloth and putting it directly on the tooth or gum tissue where it hurts. The numbing effect of the cold, along with an appropriate dose of aspirin, usually provides temporary relief.

In young adults, an erupting 3rd molar (Wisdom tooth), especially if it is impacted, can cause the jaw to swell and be quite painful. Often the gum around the tooth will show signs of infection. Temporary relief can be had by giving aspirin or some other painkiller and by dissolving an aspirin in half a glass of warm water and holding this solution in the mouth over the sore gum. AGAIN DO NOT PLACE A TABLET DIRECTLY OVER THE GUM OR CHEEK OR USE THE ASPIRIN SOLUTION ANY STRONGER THAN RECOMMENDED TO PREVENT BURNING THE TISSUE. The swelling of the jaw can be reduced by using an ice pack on the outside of the face at intervals of ten minutes on and ten minutes off.

If you have any concerns relating to where by and how to use Washington DC Dentist, you can call us at our own web-site.

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