Abstract: Massive multiple-input multiple-output (MIMO) opens up new avenues for enabling highly efficient random access (RA) by offering abundance of spatial degrees of freedom. In this paper, we ...

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JMathArray provides classes with static methods for basic math in Java. Random number generations is based on RngPack?, linear algebra is based on Jama. List of static methods applicable on int and ...

Will Kenton is an expert on the economy and investing laws and regulations. He previously held senior editorial roles at Investopedia and Kapitall Wire and holds a MA in Economics from The New School ...

Abstract: We find the exact rate for convergence in probability of products of independent, identically distributed symmetric, stochastic matrices. It is well-known that if the matrices have positive ...

Tabletop games, from the roll of a die in a fantasy role-playing game (RPG) to the strategic placement of cards in a complex board game, are deeply rooted in probability. The comprehension of the ...

There are 36 cards labeled with the numbers 1 through 36 and then placed face down on a table. If four cards are revealed one after the other, what is the probability that each card’s number is larger ...

Here is a table of the values for the cumulative distribution function of the standard normal distribution. These will be used to approximated binomial random variables. Here is another table with ...

Driven by new technology called OpenAI o1, the chatbot can test various strategies and try to identify mistakes as it tackles complex tasks. By Cade Metz Reporting from San Francisco Online chatbots ...