This second edition of Mathematical Geosciences book adds five new topics: Solution
equations with uncertainty, which proposes two novel methods for solving nonlinear
geodetic equations as stochastic variables when the parameters of these equations
have uncertainty characterized by probability distribution. The first method, an algebraic
technique, partly employs symbolic computations and is applicable to polynomial systems
having different uncertainty distributions of the parameters. The second method, a
numerical technique, uses stochastic differential equation in Ito form; Nature Inspired
Global Optimization where Meta-heuristic algorithms are based on natural phenomenon
such as Particle Swarm Optimization. This approach simulates, e.g., schools of fish
or flocks of birds, and is extended through discussion of geodetic applications. Black
Hole Algorithm, which is based on the black hole phenomena is added and a new variant
of the algorithm code is introduced and illustrated based on examples; The application
of the Gröbner Basis to integer programming based on numeric symbolic computation
is introduced and illustrated by solving some standard problems; An extension of the
applications of integer programming solving phase ambiguity in Global Navigation Satellite
Systems (GNSSs) is considered as a global quadratic mixed integer programming task,
which can be transformed into a pure integer problem with a given digit of accuracy.
Three alternative algorithms are suggested, two of which are based on local and global
linearization via McCormic Envelopes; and Machine learning techniques (MLT) that offer
effective tools for stochastic process modelling. The Stochastic Modelling section
is extended by the stochastic modelling via MLT and their effectiveness is compared
with that of the modelling via stochastic differential equations (SDE). Mixing MLT
with SDE also known as frequently Neural Differential Equations is also introduced
and illustratedby an image classification via a regression problem.
