An Introduction to Probability Theory and its Applications, Volume I

TL;DR: This paper discusses the different approaches to the teaching of a first course in stochastic processes to researchers, and proposes for the core topics of such a course and ways of teaching them.

TL;DR: Distributed dynamic channel allocation (DCA) algorithms for wireless cellular networks are considered, showing significant reductions in access blocking probability, when an aggressive, rather than timid, access algorithm is used.

TL;DR: It is shown that some sequences admitted by Von Mises as "random" in fact manifest a certain kind of systematicity, and an expanded version of the latter, alternative argument is provided.

TL;DR: Results of this study illustrate that both reuse methods can be strategically integrated into design education and architectural practice, supporting learning and use of algorithmic design systems in architecture.

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.