Recursion is the generation of an infinite range of expressions from a finite set of elements, whereas the theory of mind enables an individual to assess the mental state of other individuals.
Mathematics shares with language an essential reliance on the human capacity for recursion, permitting the generation of an infinite range of embedded expressions from a finite set of symbols.
Our modelling approach involves the discretization and digitization of temporal mRNA expression profiles into a finite number of levels (states), which are defined by discretization of continuous/analogue gene expression levels (Step 1 & 2, Figure 2 and Methods).
Initially, a model approach is employed to yield an expression for the response of a finite system under Born-von Kármán boundary conditions.
Second, the discrete dimensional-convolution procedure, which transforms the solution to the non-recursive expression of n, including a finite number of elementary operations and functions.
Our approach (1) allows the expression of the finite element problem in a language which is close to the mathematical formulation of the problem, (2) guarantees the automatic generation and efficient execution of parallel optimised low-level computer code and (3) is flexible enough to support different abstraction levels and give the programmer control over details of the preconditioner.
The mathematical expression for the admittance response of a finite fractal electrode depends on diffusion length (√D/ω), charge transfer resistance (RCT) and its fractal morphological characteristics.
According to Poincaré [2], to integrate a differential equation is to find for the general solution an expression, possibly multivalued, in terms of a finite number of functions.
In that way we develop two approaches for the expressions with a finite number of terms.
The obtained closed-form SEP expressions contain a finite sum of single integrals with finite limits and an integrand composed of elementary (exponential, trigonometric, and/or power) functions, which can be easily and accurately evaluated numerically.
