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QUANTUM BIOLOGY - EXAMPLE 33.9 : (a) Let ^ be the symbol of power where 10 ^ 1 = 10, 10 ^ 2 = 100, 10 ^ 3 = 1000 etc. Total energy consumption of the brain is about 25 Watts, whereas a Blue Gene computer requires 1.5 Mega Watts. Blue Gene computer performs at 1 petaflop. In a human body, there are approximately 10 ^ 16 synapse operations per second i. e. at least 10 petaflops. Prove by calculations that a human brain is more energy efficient than a Blue Gene computer. (b) Quantum effects and quantum entanglement in the brain are identical to quantum gravity and string theory. If one is true, the other is true. What conclusion can be made if quantum effects in the brain and quantum gravity are true?

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ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.2 : (a) In the pricing of a coupon bond, the formula is : P = c / (1 + r) + (c + B) / [ (1 + r) (1 + r) ] for 2 years to maturity, where c = annual coupon payment (in dollars, not a percent), B = par value, P = purchase price. Five years ago someone bought a 20 year coupon bond and would like to get rid of it now : A coupon rate of 7 %, it matures in exactly 2 years, par value is $1000, current interest rate is 5 %. (i) Find the value of c. (ii) Find the value of r or interest rate. (iii) Find the value of P. (iv) Guess the formula for P when the maturity period is 3 years, if such formula for 1 year duration is P = (c + B) / (1 + r). (b) In lemma of Ito on a Forward, recall that a forward contract is priced at : ln F = ln S + rT. Find the value of F in 5 decimal points when S = $100, r = interest rate = 0.05 / year, T = duration = 1 year.

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