No importance ranking can be simultaneously faithful, stable, and complete under symmetry — at any level of a model, from input features to internal circuits — and we prove it in Lean 4. If you have ...

The central limit theorem started as a bar trick for 18th-century gamblers. Now scientists rely on it every day. No matter where you look, a bell curve is close by. Place a measuring cup in your ...

👉 Learn how to solve for the unknown in a triangle divided internally such that the division is parallel to one of the sides of the triangle. The triangle proportionality theorem states that if a ...

Abstract: This paper considers the consensus behavior of a spatially distributed 3-D dynamical network composed of heterogeneous agents: leaders and followers, in which the leaders have the preferred ...

Abstract: A new value set approach is developed to examine the robust stability analysis of power systems, such as power systems with wind power penetration. The new approach has several advantages ...

The balance between natural selection and mutation in populations with complex spatial structures is complicated to understand. Qualitatively, it is known that when selection acts sufficiently weakly, ...

Mathematics Department, Egerton University, Egerton, Kenya. Alternative methods for constructing confidence interval for p have been proposed, such as the Wilson Score, Clopper-Pearson and ...

For mathematicians and computer scientists, 2020 was full of discipline-spanning discoveries and celebrations of creativity. Several long-standing problems yielded to sustained collaboration, ...