Palindromic complexity of infinite words associated with simple
... set, it must contain a palindrome p of length ≥ R(n). Since p contains all factors of u of length n, and p is a palindrome, it contains with every w such that |w| = n also its reversal w. e Thus w e ∈ L(u). This consideration if valid for all n and thus the statement of the lemma is proved. ...
... set, it must contain a palindrome p of length ≥ R(n). Since p contains all factors of u of length n, and p is a palindrome, it contains with every w such that |w| = n also its reversal w. e Thus w e ∈ L(u). This consideration if valid for all n and thus the statement of the lemma is proved. ...
A Poisoned Dart for Conditionals
... random variable that takes value 1 at worlds where p and q are both true, 0 at worlds where p is true and q false, and P(q | p) at worlds where p is false. So thinking of C as such a random variable, it takes the value 1 at ½, 0 throughout (1/2, 1], and P(1/2 | [1/2, 1]) = 0 throughout [0, ½). Its o ...
... random variable that takes value 1 at worlds where p and q are both true, 0 at worlds where p is true and q false, and P(q | p) at worlds where p is false. So thinking of C as such a random variable, it takes the value 1 at ½, 0 throughout (1/2, 1], and P(1/2 | [1/2, 1]) = 0 throughout [0, ½). Its o ...
Symmetry and Probability - Academic Commons
... the earliest theorists of probability were able to justify the initial assumptions of equiprobability which allowed them to compute the probabilities of more complex events using combinatorial methods, i.e., by simply counting cases. Nevertheless, in spite of the role that symmetry played in the ear ...
... the earliest theorists of probability were able to justify the initial assumptions of equiprobability which allowed them to compute the probabilities of more complex events using combinatorial methods, i.e., by simply counting cases. Nevertheless, in spite of the role that symmetry played in the ear ...
A new resolution of the Judy Benjamin problem
... Then he would effectively have told the platoon that it is not in Red Second Company area. And this, the authors contend, would have allowed Judy to conditionalize on ¬R ∨ ¬S, with the obvious result that Pr1 (¬R) = 2/3 and Pr1 (R) = 1/3, where Pr1 is again her new degrees-of-belief function after t ...
... Then he would effectively have told the platoon that it is not in Red Second Company area. And this, the authors contend, would have allowed Judy to conditionalize on ¬R ∨ ¬S, with the obvious result that Pr1 (¬R) = 2/3 and Pr1 (R) = 1/3, where Pr1 is again her new degrees-of-belief function after t ...
What has been will be again : A Machine Learning Approach to the Analysis of Natural Language
... in the case of handwriting. A major diculty in the analysis of such temporal structures is the need to separate the intrinsic dynamics of the system from the more relevant information of the (unknown) control signals. A common practice is to rst preprocess the input signal and transform it to a mo ...
... in the case of handwriting. A major diculty in the analysis of such temporal structures is the need to separate the intrinsic dynamics of the system from the more relevant information of the (unknown) control signals. A common practice is to rst preprocess the input signal and transform it to a mo ...
2 - Scientific Research Publishing
... through infinity, and that quantities whether increasing from zero or decreasing come back on themselves and return to the same destination 0, so that quantities greater than infinity are thereby less than zero and quantities less than infinity coincide with quantities greater than zero. Dixit Euler ...
... through infinity, and that quantities whether increasing from zero or decreasing come back on themselves and return to the same destination 0, so that quantities greater than infinity are thereby less than zero and quantities less than infinity coincide with quantities greater than zero. Dixit Euler ...
Infinite monkey theorem
The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare.In this context, ""almost surely"" is a mathematical term with a precise meaning, and the ""monkey"" is not an actual monkey, but a metaphor for an abstract device that produces an endless random sequence of letters and symbols. One of the earliest instances of the use of the ""monkey metaphor"" is that of French mathematician Émile Borel in 1913, but the first instance may be even earlier. The relevance of the theorem is questionable—the probability of a universe full of monkeys typing a complete work such as Shakespeare's Hamlet is so tiny that the chance of it occurring during a period of time hundreds of thousands of orders of magnitude longer than the age of the universe is extremely low (but technically not zero). It should also be noted that real monkeys don't produce uniformly random output, which means that an actual monkey hitting keys for an infinite amount of time has no statistical certainty of ever producing any given text.Variants of the theorem include multiple and even infinitely many typists, and the target text varies between an entire library and a single sentence. The history of these statements can be traced back to Aristotle's On Generation and Corruption and Cicero's De natura deorum (On the Nature of the Gods), through Blaise Pascal and Jonathan Swift, and finally to modern statements with their iconic simians and typewriters. In the early 20th century, Émile Borel and Arthur Eddington used the theorem to illustrate the timescales implicit in the foundations of statistical mechanics.