184
N. Y. Quintero
2 Materials and Methods
2.1 Data
The objects to be ranked are 83 microorganisms with potential as U trappers. They
are characterised by three attributes according to (Quintero et al. 2017). These
attributes are: U uptake capacity, UC, percentage of U removal (%M) and time
requested for removing the U input, t (Bruggemann et al. 2004). Table 1 shows
the attributes of 83 microorganisms used in the current study (Quintero et al. 2018);
this table includes the 38 prokaryotes studied by (Quintero et al. 2017).
2.2 Methodology Selected in the Current Study
Given a finite set of microorganisms it is posible to define partial order relations
among them in several ways, whence partial order theory has become a powerful
technique in many fields, including the biotechnological one as in the current case
(Quintero et al. 2017).
2.2.1 Hasse Diagram Technique
Here, we only give a short description, for more details see (Bruggemann and Patil
2011; Bruggemann and Halfon 1999).
A Hasse diagram (HD) is a visual representation of a partially ordered set (poset)
underlying the objects and their attributes. If X is the set gathering the microorganisms with potential as U trappers and each microorganism x is characterised by
attributes q, it is possible to order these microorganisms by ordering their atributes
(Bruggemann and Patil 2011).
Hence, if it is established that q i (x) ≤ q i (y), for all i with x, y ∈ X, then x y. This
also holds if at least for one attribute q j (x) < q j (y), while for all others q(x) = q(y).
The relation is a binary relation meeting: x x; if x y and y x⇒ x = y; and
if x y and y z ⇒ x z; i.e. is reflexive, antisymmetric and transitive, which
makes, an order relation (Trotter 1992).
Any two microorganisms x, y are said to be comparable whenever x y or y x,
otherwise they are incomparable (Bruggemann and Patil 2011). The HD shows those
comparabilities that cannot be obtained from others, i.e. those that are not obtained
by transitivities and it constitutes a map of order relationships for the objects. In the
HD, if a sequence of lines is connecting two microorganisms strictly either in the
upward or the downward direction, the microorganisms are considered comparable,
otherwise, they are incomparable (Bruggemann and Patil 2011).
From the HD, several sets can be derived (Bruggemann and Carlsen 2011;
Bruggemann et al. 2004):
N. Y. Quintero
2 Materials and Methods
2.1 Data
The objects to be ranked are 83 microorganisms with potential as U trappers. They
are characterised by three attributes according to (Quintero et al. 2017). These
attributes are: U uptake capacity, UC, percentage of U removal (%M) and time
requested for removing the U input, t (Bruggemann et al. 2004). Table 1 shows
the attributes of 83 microorganisms used in the current study (Quintero et al. 2018);
this table includes the 38 prokaryotes studied by (Quintero et al. 2017).
2.2 Methodology Selected in the Current Study
Given a finite set of microorganisms it is posible to define partial order relations
among them in several ways, whence partial order theory has become a powerful
technique in many fields, including the biotechnological one as in the current case
(Quintero et al. 2017).
2.2.1 Hasse Diagram Technique
Here, we only give a short description, for more details see (Bruggemann and Patil
2011; Bruggemann and Halfon 1999).
A Hasse diagram (HD) is a visual representation of a partially ordered set (poset)
underlying the objects and their attributes. If X is the set gathering the microorganisms with potential as U trappers and each microorganism x is characterised by
attributes q, it is possible to order these microorganisms by ordering their atributes
(Bruggemann and Patil 2011).
Hence, if it is established that q i (x) ≤ q i (y), for all i with x, y ∈ X, then x y. This
also holds if at least for one attribute q j (x) < q j (y), while for all others q(x) = q(y).
The relation is a binary relation meeting: x x; if x y and y x⇒ x = y; and
if x y and y z ⇒ x z; i.e. is reflexive, antisymmetric and transitive, which
makes, an order relation (Trotter 1992).
Any two microorganisms x, y are said to be comparable whenever x y or y x,
otherwise they are incomparable (Bruggemann and Patil 2011). The HD shows those
comparabilities that cannot be obtained from others, i.e. those that are not obtained
by transitivities and it constitutes a map of order relationships for the objects. In the
HD, if a sequence of lines is connecting two microorganisms strictly either in the
upward or the downward direction, the microorganisms are considered comparable,
otherwise, they are incomparable (Bruggemann and Patil 2011).
From the HD, several sets can be derived (Bruggemann and Carlsen 2011;
Bruggemann et al. 2004):