SageMath is a free, open-source mathematical software system based on the Python programming language. It covers a wide range of mathematical areas including algebra, calculus, number theory, geometry ...

BRAPH 2.0 is a comprehensive software package for the analysis and visualization of brain connectivity data, offering flexible customization, rich visualization capabilities, and a platform for ...

You may have seen the “no-lift pencil” puzzles online — challenges that ask you to draw a shape without lifting your pencil ...

Inspired by the skill-text bipartite graph model proposed by Arora and Goyal for modeling semantic languages, we develop a mathematical theory to explain the emergence of learned skills, taking the ...

In the default model, the graph representing each individual enhancer can be arbitrarily complicated. To show how the ABC Score formula can arise from the default model, we need to impose the further ...

According to mathematical legend, Peter Sarnak and Noga Alon made a bet about optimal graphs in the late 1980s. They’ve now ...

MR. LOVE'S treatise is the necessary complement to Todhunter and Pearson's “History of the Theory of Elasticity,” in which an abstract is given of all the most important original memoirs ...

The necessity for these two additional assumptions, which appear to be of an arbitrary character, has led some to consider Fresnel's theory as ... equations of mathematical physics, which was ...

That was 30 years ago this month, making the moment ripe for taking stock: Is string theory revealing reality’s deep laws? Or, as some detractors have claimed, is it a mathematical mirage that ...

A coordinate plane with a plotted graph representing a function, highlighting its fluctuations and extrema. Showcases a grid with clearly labeled axes and dynamic curve shapes. Royalty-free licenses ...

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Coordinating complicated interactive systems, whether it's the different modes of transportation in a city or the various ...