Random Constraint Satisfaction
... In this paper we show that as long as the number of permissible pairs of value assignments in each constraint is any constant fraction of all possible pairs, then as the number of variables increases, the probability that a solution exists tends to 0. Obviously, this implies that a threshold phenome ...
... In this paper we show that as long as the number of permissible pairs of value assignments in each constraint is any constant fraction of all possible pairs, then as the number of variables increases, the probability that a solution exists tends to 0. Obviously, this implies that a threshold phenome ...
4 Sums of Independent Random Variables
... Proposition 4.7. (Strong Markov Property) Let X 1 , X 2 , . . . be independent, identically distributed random variables and let ø be a finite stopping time (i.e., a stopping time such that P {ø < 1} = 1). Then the random variables X ø+1 , X ø+2 , . . . are independent, identically distributed and h ...
... Proposition 4.7. (Strong Markov Property) Let X 1 , X 2 , . . . be independent, identically distributed random variables and let ø be a finite stopping time (i.e., a stopping time such that P {ø < 1} = 1). Then the random variables X ø+1 , X ø+2 , . . . are independent, identically distributed and h ...
On Worst-Case to Average-Case Reductions for NP Problems
... hierarchy collapses to the third level. We first prove the result for the special case in which the distribution D is uniform (Theorem 17). Then, using reductions by Impagliazzo and Levin [IL90] and by Ben-David and others [BCGL89], we show that the same is true even if the reduction assumes a good ...
... hierarchy collapses to the third level. We first prove the result for the special case in which the distribution D is uniform (Theorem 17). Then, using reductions by Impagliazzo and Levin [IL90] and by Ben-David and others [BCGL89], we show that the same is true even if the reduction assumes a good ...
Central Limit Theorems in Ergodic Theory
... would like to use the expression - even in connection with a sequence of random variables that only converges in probability - that we ’take a point where the convergence holds’. By this we are going to mean the following. It is wellknown that a sequence of random variables converges in probability ...
... would like to use the expression - even in connection with a sequence of random variables that only converges in probability - that we ’take a point where the convergence holds’. By this we are going to mean the following. It is wellknown that a sequence of random variables converges in probability ...
10-AntColony
... dij = the tour cost from city i to city j (edge weight) Ant move from one city i to the next j with some transition probability. ...
... dij = the tour cost from city i to city j (edge weight) Ant move from one city i to the next j with some transition probability. ...
Computing Conditional Probabilities in Large Domains by
... P(raining) = 0.1. If we condition the probability on the knowledge that we are in Pittsburgh we may find P(raining|Pittsburgh) = 0.3. Sometimes the knowledge of an evidence variable provides no additional information for computing the probability of a hidden variable. For example, when computing the ...
... P(raining) = 0.1. If we condition the probability on the knowledge that we are in Pittsburgh we may find P(raining|Pittsburgh) = 0.3. Sometimes the knowledge of an evidence variable provides no additional information for computing the probability of a hidden variable. For example, when computing the ...
Stochastic Tools for Mathematics and Science Alexandre J. Chorin
... engineering. The course has not endeavored to present a full, rigorous theory of probability and its applications, but rather to provide mathematics students with some inkling of the many beautiful applications of probability, as well as introduce the nonmathematical students to the general ideas be ...
... engineering. The course has not endeavored to present a full, rigorous theory of probability and its applications, but rather to provide mathematics students with some inkling of the many beautiful applications of probability, as well as introduce the nonmathematical students to the general ideas be ...
