The abundance and environment of dark matter haloes
  An open question in cosmology and the theory of structure formation is to
what extent does environment affect the properties of galaxies and haloes. The
present paper aims at shedding light on this problem. The paper focuses on the
analysis of a dark matter only simulation and it addresses the issue of how the
environment affects the abundance of haloes, which are are assigned four
attributes: their virial mass, an ambient density calculated with an aperture
that scales with $R_{vir}$ ($\Delta_M$), a fixed-aperture ($\Delta_R$) ambient
density, and a cosmic web classification (i.e. voids, sheets, filaments, and
knots, as defined by the V--web algorithm). $\Delta_M$ is the mean density
around a halo evaluated within a sphere of a radius of $5$\rvir, where \rvir\
is the virial radius. $\Delta_R$ is the density field Gaussian smoothed with
$R=4h^{-1}$Mpc, evaluated at the center of the halo.
  The main result of the paper is that the difference between haloes in
different web elements stems from the difference in their mass functions, and
does not depend on their adaptive-aperture ambient density. A dependence on the
fixed-aperture ambient density is induced by the cross correlation between the
mass of a halo and its fixed-aperture ambient density.
