A calculation of the probability of assembling the first protocell
... container. If assembly of life’s components first took place on a catalytic surface which then led to a selfreproducing ensemble, this might be more probable than what we are proposing as a single step from molecules in solution to an organic protocell. As such, our calculations may suggest some kin ...
... container. If assembly of life’s components first took place on a catalytic surface which then led to a selfreproducing ensemble, this might be more probable than what we are proposing as a single step from molecules in solution to an organic protocell. As such, our calculations may suggest some kin ...
Bernoulli trial
... · underlying causes of phenomena are unknown, but small effects are added into an observable score ...
... · underlying causes of phenomena are unknown, but small effects are added into an observable score ...
Parallel and Concurrent Security of the HB and HB Protocols
... i k As,ε k Pr s ← {0, 1} : M (1 ) = s ≥ δ, and furthermore M runs in time at most t and makes at most q queries to its oracle.3 In asymptotic terms, in the standard way, the LPNε problem is “hard” if every probabilistic polynomial-time algorithm M solves the LPNε problem with only negligible probabi ...
... i k As,ε k Pr s ← {0, 1} : M (1 ) = s ≥ δ, and furthermore M runs in time at most t and makes at most q queries to its oracle.3 In asymptotic terms, in the standard way, the LPNε problem is “hard” if every probabilistic polynomial-time algorithm M solves the LPNε problem with only negligible probabi ...
Catalyst-assisted Probabilistic Entanglement Transformation
... to that of a catalyst in a chemical process. The mathematical structure of this phenomenon, so called catalystassisted entanglement transformation, was carefully examined by Daftuar and Klimesh [12]. They found that there does not exist an upper bound on the dimension of catalysts that should be con ...
... to that of a catalyst in a chemical process. The mathematical structure of this phenomenon, so called catalystassisted entanglement transformation, was carefully examined by Daftuar and Klimesh [12]. They found that there does not exist an upper bound on the dimension of catalysts that should be con ...
Connectivity Properties of Random Subgraphs of the Cube - IME-USP
... which is in itself a pleasant result, although in view of the analogous result for ordinary random graph processes (se Bollobás and Thomason [6]), and a result of Dyer, Frieze, and Foulds [7], it is not too unexpected. In [7], the authors study the connectivity of random subgraphs of the n-cube obt ...
... which is in itself a pleasant result, although in view of the analogous result for ordinary random graph processes (se Bollobás and Thomason [6]), and a result of Dyer, Frieze, and Foulds [7], it is not too unexpected. In [7], the authors study the connectivity of random subgraphs of the n-cube obt ...
Ch.3 Random number generators
... Gaussian numbers (e.g., randn in MATLAB) because it is very efficient. It is essentially the rejection method applied to segments of the Gaussian curve (see diagram). First one of the rectangles is selected at random (as they have equal area), then a second random number is used to decide if the x v ...
... Gaussian numbers (e.g., randn in MATLAB) because it is very efficient. It is essentially the rejection method applied to segments of the Gaussian curve (see diagram). First one of the rectangles is selected at random (as they have equal area), then a second random number is used to decide if the x v ...
Topic 4
... coin has been flipped 100 times, and has come down heads 47 times. Then the probability of the coin’s coming down heads, according to the relative frequency conception of probability, is 0.47. The Relative Frequency in the Limit Conception of Probability The idea of defining a concept of probability ...
... coin has been flipped 100 times, and has come down heads 47 times. Then the probability of the coin’s coming down heads, according to the relative frequency conception of probability, is 0.47. The Relative Frequency in the Limit Conception of Probability The idea of defining a concept of probability ...
A detailed interpretation of probability, and its link with quantum
... probability, Laplace, Fermat, Venn, von Mises, etc. Clearly, in developing his theory Kolomogorov1 was much inspired by these interpretations, so much that one can read ([2], p. 2): “Kolmogorov himself followed a rather vague intuition of frequentist probability, an attitude most likely to be found ...
... probability, Laplace, Fermat, Venn, von Mises, etc. Clearly, in developing his theory Kolomogorov1 was much inspired by these interpretations, so much that one can read ([2], p. 2): “Kolmogorov himself followed a rather vague intuition of frequentist probability, an attitude most likely to be found ...
ON BERNOULLI DECOMPOSITIONS FOR RANDOM VARIABLES
... As is the case of G in (2.14), the functions Y1 and Y2 are made into random variables by assigning to them the joint probability distribution which is induced by Lebesgue measure on [0, 1]. Their marginal distributions satisfy (2.11), since for any continuous function φ ∈ C(R) Z 1 Z 1 (1 − p) φ(Y1 ( ...
... As is the case of G in (2.14), the functions Y1 and Y2 are made into random variables by assigning to them the joint probability distribution which is induced by Lebesgue measure on [0, 1]. Their marginal distributions satisfy (2.11), since for any continuous function φ ∈ C(R) Z 1 Z 1 (1 − p) φ(Y1 ( ...
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.