To address these issues, this paper is therefore concerned with the development of a visual language that is prescribed and to be used by product designers to annotate paper-based sketches such that the form geometry semantics can be formally represented; parsing the annotated sketch allows for the automatic generation of 3D virtual models in CAD.
Although the incorporation of these disjunctive interpretations of annotations would lead to a formally consistent knowledge base, incorrectly annotated model entities would not cause an inconsistency anymore and therefore prevent us from automatically identifying incorrect annotations through automated reasoning.
The phylotype root must have a unique annotation, say A, which lasted until extant phylotype members that are annotated by A. Formally, within a clade with root r, every taxon x sharing the same annotation A as r, and for which A is conserved along the path from r to x, belongs to the phylotype defined by r and A (assuming the MRCA condition is fulfilled).
Formally, a sound query is annotated using tags from a vocabulary of semantic concepts.
More formally, we define a node as annotated when a signed real number is assigned to the node, representing an experimental data value (e.g. the expression ratio of a gene between a disease and a normal state, obtained from transcriptomic profiling).
Although it has not been formally demonstrated and in spite of being annotated as ARF-3 in the T. brucei database (Tb927.7.6230, GeneDB http://www.genedb.org/), this TbARL-1 is very likely the functional homologue/orthologue of LdARL-1 given the synteny of the homologous chromosomal region of several trypanosomatids (Fig S1).
More formally: R 0 a (u ) = ∞ if u is annotated with a and 0 otherwise.
Expressed formally, let us consider drug-disease relationships, with scores X s, drug annotation levels X c and disease annotation levels X d, where the annotation level is the number of MeSH terms annotated to articles in MEDLINE for the drug or disease.
Symbol a i represents either a position in X, or a gap annotated with the position of the nearest non-gap symbol on the left; formally a i ∈ {1, …, n} ∪ {-0, -1, …, - n }.
