That’s because a new framework is improving the probabilistic reasoning of LLMS like ChatGPT and Gemini. School of ...

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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 a closed form expression for the joint probability mass function of the occupation times for a Three-State Markov chain. Our representation extends the long-standing result for a ...

Function raises $10M led by Galaxy Digital to help institutions earn yield on bitcoin using FBTC, a fully backed, custody-safe DeFi product. Function, a crypto infrastructure startup, has raised $10 ...

Journal of Applied Probability, Vol. 58, No. 3 (SEPTEMBER 2021), pp. 621-636 (16 pages) Signatures are useful in analyzing and evaluating coherent systems. However, their computation is a challenging ...

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 ...

Abstract: This paper presents an analysis of the average bit error probability (ABEP) based on the moment generating function (MGF) over the Beaulieu-Xie fading ...

Abstract: The choice of activation function in deep learning is crucial to the performance of neural networks. The activation function used in conventional deep learning remains unchanged for neural ...

Function-calling agent models, a significant advancement within large language models (LLMs), face the challenge of requiring high-quality, diverse, and verifiable datasets. These models interpret ...