The paradox of biological diversity is the key problem of theoretical ecology. The paradox consists in the contradiction between the competitive exclusion principle and the observed biodiversity. The principle is important as the basis for ecological theory. On a relatively simple model we show a mechanism of indefinite coexistence of complete competitors which violates the known formulations o...

The Pauli Exclusion Principle is a basic principle of Quantum Mechanics, and its validity has never been seriously challenged. However, given its fundamental standing, it is very important to check it as thoroughly as possible. Here we describe the VIP (VIolation of the Pauli exclusion principle) experiment, an improved version of the Ramberg and Snow experiment (E. Ramberg and G. Snow, Phys. L...

Abstract We present two fast algorithms which apply inclusion–exclusion principle to sum over the bosonic diagrams in bare diagrammatic quantum Monte Carlo and inchworm method, respectively. In case of Carlo, proposed algorithm gives an extension work [2018 Inclusion–exclusion for many-body diagrammatics Phys. Rev. B 98 115152] from fermionic systems. prove that reduce computational complexity ...