PROBABILISTIC ALGORITHMIC RANDOMNESS §1. Introduction
... strategies correspond to algorithms that can actually be carried out. The only non-algorithmic aspect is the use of randomness to decide whether to bet or not at each step. Furthermore, the fact that betting strategies are allowed to use randomness is entirely natural. In practical terms, randomness ...
... strategies correspond to algorithms that can actually be carried out. The only non-algorithmic aspect is the use of randomness to decide whether to bet or not at each step. Furthermore, the fact that betting strategies are allowed to use randomness is entirely natural. In practical terms, randomness ...
Random Permutation Statistics and An Improved Slide
... j8 , the faster will be the attack and both the best-case and average complexity of the whole attack will be improved. This is achieved as follows. We store the triples p, c, (k15 , . . . , k0 ) in a data structure keyed by (k15 , . . . , k0 ). (For instance, we can have an array of size 216 , where ...
... j8 , the faster will be the attack and both the best-case and average complexity of the whole attack will be improved. This is achieved as follows. We store the triples p, c, (k15 , . . . , k0 ) in a data structure keyed by (k15 , . . . , k0 ). (For instance, we can have an array of size 216 , where ...
What is Probability? Patrick Maher August 27, 2010
... It has often been asserted that “probability” means some person’s degrees of belief. Here are a few examples: By degree of probability we really mean, or ought to mean, degree of belief. (de Morgan 1847, 172) Probability measures the confidence that a particular individual has in the truth of a part ...
... It has often been asserted that “probability” means some person’s degrees of belief. Here are a few examples: By degree of probability we really mean, or ought to mean, degree of belief. (de Morgan 1847, 172) Probability measures the confidence that a particular individual has in the truth of a part ...
TAIL BOUNDS FOR GAPS BETWEEN EIGENVALUES 1
... p. We denote by An (p) the (zero-one) adjacency matrix of G(n, p). Random matrix with arbitrary mean. We consider a random Hermitian matrix Mn of the form Mn := Fn +Xn , where F = Fn is a deterministic symmetric matrix of size n and of norm kFn k2 = nO(1) , and Xn is a random Hermitian matrix where ...
... p. We denote by An (p) the (zero-one) adjacency matrix of G(n, p). Random matrix with arbitrary mean. We consider a random Hermitian matrix Mn of the form Mn := Fn +Xn , where F = Fn is a deterministic symmetric matrix of size n and of norm kFn k2 = nO(1) , and Xn is a random Hermitian matrix where ...
Method - Psychology Department
... controversial because the statistical analysis did not allow each participant to have a different true preference order. Recently, however, it has been theorized that an inherently intransitive process governs risky decision making. This paper uses a relatively new statistical technique for testing ...
... controversial because the statistical analysis did not allow each participant to have a different true preference order. Recently, however, it has been theorized that an inherently intransitive process governs risky decision making. This paper uses a relatively new statistical technique for testing ...
Chapter 5 - WordPress.com
... Statistician Reads the Sports Pages,” pp. 17-21,) Hal Stern investigated the probabilities that a particular horse will win a race. He reports that these probabilities are based on the amount of money bet on each horse. When a probability is given that a particular horse will win a race, is this emp ...
... Statistician Reads the Sports Pages,” pp. 17-21,) Hal Stern investigated the probabilities that a particular horse will win a race. He reports that these probabilities are based on the amount of money bet on each horse. When a probability is given that a particular horse will win a race, is this emp ...
(preprint)
... in molecular biology labs is similarity search. That is, to compare one DNA sequence against another, or to a database, to 1nd any similar regions between them. Many programs have been developed for the task. These include FASTA [9], SIM [7], the Blast family [1,2,6,15,18] SENSEI [14], and recently ...
... in molecular biology labs is similarity search. That is, to compare one DNA sequence against another, or to a database, to 1nd any similar regions between them. Many programs have been developed for the task. These include FASTA [9], SIM [7], the Blast family [1,2,6,15,18] SENSEI [14], and recently ...
probability models for economic decisions
... The difficulties of decision-making under uncertainty are familiar to everyone. We all regularly have to make decisions where we lack important information about factors that could significantly affect the outcomes of our decisions. Decision analysis is the study of general techniques for quantitati ...
... The difficulties of decision-making under uncertainty are familiar to everyone. We all regularly have to make decisions where we lack important information about factors that could significantly affect the outcomes of our decisions. Decision analysis is the study of general techniques for quantitati ...
Ars Conjectandi
Ars Conjectandi (Latin for The Art of Conjecturing) is a book on combinatorics and mathematical probability written by Jakob Bernoulli and published in 1713, eight years after his death, by his nephew, Niklaus Bernoulli. The seminal work consolidated, apart from many combinatorial topics, many central ideas in probability theory, such as the very first version of the law of large numbers: indeed, it is widely regarded as the founding work of that subject. It also addressed problems that today are classified in the twelvefold way, and added to the subjects; consequently, it has been dubbed an important historical landmark in not only probability but all combinatorics by a plethora of mathematical historians. The importance of this early work had a large impact on both contemporary and later mathematicians; for example, Abraham de Moivre.Bernoulli wrote the text between 1684 and 1689, including the work of mathematicians such as Christiaan Huygens, Gerolamo Cardano, Pierre de Fermat, and Blaise Pascal. He incorporated fundamental combinatorial topics such as his theory of permutations and combinations—the aforementioned problems from the twelvefold way—as well as those more distantly connected to the burgeoning subject: the derivation and properties of the eponymous Bernoulli numbers, for instance. Core topics from probability, such as expected value, were also a significant portion of this important work.