The reduced stress tensor (bar {boldsymbol {sigma }}^) obtained by the introduced – mean field homogenization based – rheology model (2) and (13) is denoted for the comparison with (bar {sigma }_{text {mf}}), and the equation through which it is defined, is given here for convenience bar{boldsymbol{sigma}}^_{text{mf}} = bar{mathbb{V}} [bar{boldsymbol{D}}']/eta_{mathrm{s}}.
The concept which I am defining is not given prior to the definition itself; on the contrary, it only comes into existence as a result of that definition.
The balance between gravitational potential energy and kinetic energy allows a virial velocity to be defined, and is given by (v_{mathrm{vir}}^{2}=GM_{mathrm{vir}}/R_{mathrm{vir}}), where G is the gravitational constant, (M_{mathrm{vir}}) the virial mass, and (R_{mathrm{vir}}) the virial radius of the halo.
The phenomena between the domains is defined and the constraint set is given.
To describe the shape feature of block x in a simplified form, a new statistical parameter, V x, is defined, which is given as V x = ( σ + e ) · ( 1 + log ( 1 + | g | ) ). (21).
For "boosting", is sampled from using the distribution defined in (11), while the expert weights are defined as, where is given by (10).
A detailed explanation of how these methodologies, are mathematically defined and how they can be parameterized is given online in the Supplementary Material.
The world for this self is an object to be defined and to be given form.
Moreover, if is defined by where is given above, then is of type (R).
A representative example of how rules for anomaly detection are defined and applied is given by the LEarning Rules for Anomaly Detection (LERAD) model [25, 26].
