Fullerenes are hollow carbon molecules where each atom is connected to exactly three other atoms, arranged in pentagonal and hexagonal rings. Mathematically, they can be combinatorially modeled as ...

Born poor in colonial India and dead at 32, Ramanujan had fantastical, out-of-nowhere visions that continue to shape the field today. One afternoon in January 2011, Hussein Mourtada leapt onto his ...

To mathematicians, equations are art. Just as many are moved by a painting or piece of music, to those who appreciate and understand math, expressions of numbers, variables, operations and relations ...

From a basic probabilistic argumentation, the Zipfian distribution and Benford’s law are derived. It is argued that Zipf’s law fits to calculate the rank probabilities of identical indistinguishable ...

Abstract: In 1960 Leonhard Euler gave rigorous proof of an efficient calculation using the recurrence of partition numbers. Since the power of the variables in the recurrence is the pentagonal numbers ...

Bayesian Decision Trees provide a probabilistic framework that reduces the instability of Decision Trees while maintaining their explainability. While Markov Chain Monte Carlo methods are typically ...

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Animals detect motion using a variety of visual cues that reflect regularities in the natural world. Experiments in animals across phyla have shown that motion percepts incorporate both pairwise and ...

In the past, what we call “almost partition identities” were immediate corollaries of classical theta series identities, such as Jacobi’s triple product. Consequently, they were always of this form: ...

We describe the procedure of zeta regularization of an infinite product, in particular following the technique we introduced in previous works (13). The problem of regularizing infinite products is a ...