1 10 TEMPORAL ORGANIZATION IN CELLS 



To simplify the notation we write 



'■22^12*1 



/'22 = ^ 



The phase integrals are then 



00 00 



-pi -pt 



00 



Z^, = r e-^''i[>'->'.'°e<'+>vyi)W_yi 



—01 

 00 



2<^ ^ I g-jSA^b.-yJog (l+>',/y,)^^^ 



— Oi 



where ctj = /:2iai(^ii ^1 + ^12 '72) 



and 02 = /^i 2^2(^2 1^2 + ^22 ^2) 



It is useful to evaluate these in the limits of small and large /S. In order to do 

 this with Zp^p^, we must first reduce the quadratic in the following manner. 



hi 1 A-? + 2/ji2 -Yi .Y2 + ^22 -^2 = /^l 1 ( -^1 + ^^2 j + //22 "^2 " ^ ^ 



Now write 



Ii = (Z'n^)' '(-^i + ^7^2J, ^2 = [ f^- J ^2 (59) 



The Jacobian of this transformation is 



-lJ^'-^ = ^Vihnh22-hh) = m\'' 

 where 1//| is the determinant of the quadratic form. 

 Because ^i = (/?n^)' -■Yi+ .^.^^^ -^ 



1/2 



and ^2= \H\"m—] X2 



= ^"HB 



