An Introduction to Probability Theory and its Applications, Volume I

TL;DR: A new weighted average of several sets is introduced and a new average of sets is applied to adapt to SVFs the classical Bernstein approximation operators, and it is shown that these operators approximate continuous SVFs.

TL;DR: It is shown that the difference in their doubling rates is the quantum discord and a quantum extension of Kelly's gambling setup in the classical case gives a doubling rate that is upper bounded by the Holevo information.

TL;DR: This simplification of the www-browsing action model presented by the European Telecommunications Standards Institute can be used in numerical simulations of the packed switched telecommunication traffic and is accurate.

TL;DR: This work uses the techniques from the classical Control-Variate method ~\cite{Lavenberg} which is primarily known for variance reduction in Monte-Carlo simulations, and is able to obtain significant variance reduction at the cost of a little computational overhead.

TL;DR: This chapter discusses quantum information theory, public-key cryptography and the RSA cryptosystem, and the proof of Lieb's theorem.

TL;DR: This work addresses the problem of predicting a word from previous words in a sample of text and discusses n-gram models based on classes of words, finding that these models are able to extract classes that have the flavor of either syntactically based groupings or semanticallybased groupings, depending on the nature of the underlying statistics.

TL;DR: In this article, the authors present a case study of non-normal distribution and non-commutative joint distributions and define a set of basic combinatorics, such as non-crossing partitions, sum-of-free random variables, and products of free random variables.

TL;DR: This chapter explains why many real-world networks are small worlds and have large fluctuations in their degrees, and why Probability theory offers a highly effective way to deal with the complexity of networks, and leads us to consider random graphs.