Probability underpins AI, cryptography and statistics. However, as the philosopher Bertrand Russell said, "Probability is the most important concept in modern science, especially as nobody has the ...

We apply a promising new method from the field of representations of Lie groups to calculate integrals over unitary groups, which are important for multi-antenna communications. To demonstrate the ...

ABSTRACT: We obtain an infinite series expression for the joint probability density function of occupation times in a Three-State Markov chain. By extending the identity given by Darroch, we ...

ABSTRACT: We obtain an infinite series expression for the joint probability density function of occupation times in a Three-State Markov chain. By extending the identity given by Darroch, we ...

This investigation was supported (in part) by the U.S. Public Health Service, National Institutes of Health, grant GM-10525. Note: The article usage is presented with a three- to four-day delay and ...

In a series of recent works, an interesting quantum generative model based on parameterized instantaneous polynomial quantum (IQP) circuits has emerged as they can be trained efficiently classically ...

As is well known, the normal distribution is a key tool in probability and statistics. It can be described as a distribution that obeys a universal rule derived from one of the most important theorems ...

The Galaxy Z Fold 6’s ‘sketch to image’ tool is ridiculous, fun, and slightly worrying. The Galaxy Z Fold 6’s ‘sketch to image’ tool is ridiculous, fun, and slightly worrying. is a senior reviewer ...

The S&P 500 is commonly viewed as a benchmark for the entire U.S. stock market, and the index returned 10.1% annually over the last three decades. Historically, the S&P 500 has increased in nine out ...

Abstract: Among ultrasound images, the acoustic radiation force impulse (ARFI) image can provide information about the stiffness of the tissue using both a pushing beam and a detection beam. However, ...