Biquandles are algebraic structures with axioms motivated by the oriented Reidemeister moves of diagrams of knots and links. Biquandles have been used to define invariants of classical and virtual oriented knots and links and the results of the paper under review are motivated by effectiveness of these structures in distinguishing oriented knots and links. Singular knots and links are 4-valent spatial graphs considered up to rigid vertex isotopy, where a vertex can be thought of as the result of two strands of a knot or link getting glued together in a fixed position. A singular knot or link with exactly one singular crossing is a 2-bouquet graph. Pseudoknots are knots whose diagrams consist of usual crossings and precrossings (classical crossings where one cannot tell which strand goes on top).
The authors generalize the notion of biquandles to psyquandles and use them to define invariants of oriented singular links and pseudolinks. In addition to psyquandle counting invariants, they also introduce Alexander psyquandles and corresponding invariants such as Alexander psyquandle polynomials and Alexander-Gröbner psyquandle invariants of oriented singular knots and links. The authors define a generalization of the Alexander polynomial for oriented singular links and pseudolinks which they refer to as the Jablan polynomial and compute the invariant for all pseudoknots with up to five crossings and all 2-bouquet graphs with up to six classical crossings.