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From "Gerhard Froehlich" <g-froehl...@gmx.de>
Subject RE: Adaptive Caching [was Re: initial checkin of the Scheme code]
Date Thu, 13 Dec 2001 16:00:47 GMT
Hi,

   n 
  -- 
  \  x  = x  + x + ... + x 
  /   i    1    2         n
  --
i = 1

n = Constant or outer Parameter
i = Index only total numbers (1,2,3...)

Example:
x = 10
 1 
x = 12
 2
x = 14
 3

   3 
  -- 
  \  x  = x  + x  + x  = 10 + 12 + 14 = 36
  /   i    1    2    3
  --
i = 1

  Gerhard

--------------------------------
Beam me up... arrgh, no carrier!
--------------------------------


>-----Original Message-----
>From: Berin Loritsch [mailto:bloritsch@apache.org]
>Sent: Thursday, December 13, 2001 4:34 PM
>To: cocoon-dev@xml.apache.org
>Subject: Re: Adaptive Caching [was Re: initial checkin of the Scheme
>code]
>
>
>Stefano Mazzocchi wrote:
>
>> Talking about placing too many irons in the fire :)
>> 
>
>
>Stefano, please forgive my ignorance, as I have an Associates Degree in
>Music Recording, and not a traditional CS degree.  I haven't had the
>higher math classes you and many others have had here.
>
>I understand Algebra and Trigonometry ok, so if we can simplify these
>algorithms into a "pseudo-code" so I can wrap my head around them, I
>will be happy to jump in the discussion.  As it is now, It's going
>over my head.
>
>I understand the Calculus ideas of functions (i.e. V(r,t)).  What throws
>me are the Sigmas (I studied Ancient Greek, so I know what the letters are).
>I know they are meant to represent sums, or statistical data.  I don't know
>what the letter above the sigma or below the sigma is supposed to signify.
>
>If you don't feel up to giving me a quick math lesson so I can grok the
>concepts fully, can you point me to a resource where I can teach myself?
>
>> Thus, given
>> 
>>  r        := resource
>>  t        := time of the request
>>  V(r,t)   := validity estimation cost
>>  P(r,t)   := production cost when caching is not performed
>>  Pc(r,t)  := production cost when caching is performed
>>  l(r,t)   := lookup cost
>>  s(r,t)   := storage cost
>> 
>> and
>> 
>>  I := sequence of invalid requests time [1,n]
>>  V := sequence of valid request time [1,m]
>> 
>> we have that
>> 
>>                n
>>                --
>>  Invalid(r) =  \  (V(r,I ) + Pc(r,I ) + s(r,I ))
>>                /        i          i         i 
>>                --
>>               i = 1
>> 
>> and
>> 
>>              m
>>              --
>>  Valid(r) =  \  (V(r,I ) + L(r,I ))
>>              /        j         j
>>              --
>>            j = 1
>> 
>> and
>> 
>>             n                m
>>             --               --
>>  Ptot(r) =  \  P(r,I )   +   \  P(r,V )
>>             /       i        /       j
>>             --               --
>>           i = 1             j = 1
>> 
>
>
>
>
>-- 
>
>"They that give up essential liberty to obtain a little temporary safety
>  deserve neither liberty nor safety."
>                 - Benjamin Franklin
>
>
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