We revisit the problem of conveying classical messages by transmitting quantum states, and derive new, optimal bounds on the number of quantum bits required for this task. Much of...
In this paper, a structural theorem about toroidal graphs is given that strengthens a result of Borodin on plane graphs. As a consequence, it is proved that every toroidal graph w...
Kasteleyn stated that the generating function of the perfect matchings of a graph of genus g may be written as a linear combination of 4g Pfaffians. Here we prove this statement. ...
—We show that if a finite relational structure has a near unanimity polymorphism, then the constraint satisfaction problem with that structure as its fixed template has bounded...
We investigate algebraic, logical, and geometric properties of concepts recognized by various classes of probabilistic classifiers. For this we introduce a natural hierarchy of pr...