An Introduction to Probability Theory and its Applications, Volume I

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

TL;DR: RTP provides end-to-end network transport functions suitable for applications transmitting real-time data over multicast or unicast network services and is augmented by a control protocol (RTCP) to allow monitoring of the data delivery in a manner scalable to large multicast networks.

TL;DR: In this article, a survey of elementary applications of probability theory can be found, including the following: 1. Plausible reasoning 2. The quantitative rules 3. Elementary sampling theory 4. Elementary hypothesis testing 5. Queer uses for probability theory 6. Elementary parameter estimation 7. The central, Gaussian or normal distribution 8. Sufficiency, ancillarity, and all that 9. Repetitive experiments, probability and frequency 10. Advanced applications: 11. Discrete prior probabilities, the entropy principle 12. Simple applications of decision theory 15.

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 paper, a random walk in random environment on a supercritical Galton-Watson tree was considered, and the hitting time of generation $n was shown to be a large deviation for both quenched and annealed cases.

TL;DR: This thesis studies a special class of performance measure, defined based on Cumulative Prospect Theory (CPT), which has been used as an alternative to expected utility based performance measure for evaluating human-centric systems and introduces an abstract dynamic programming framework whose transitional measure is defined through the CPT-value.

TL;DR: Whether using only the blockchain, or the additional information in status reports, merchants can use the techniques to quantify in real-time the threat of double-spend attacks and therefore the consensus of a blockchain.

TL;DR: In this article, the authors give necessary and sufficient conditions on a graph with reversible Markov kernels to compare the results of the Calderon-Zygmund operator and the Sobolev operator.