The support vector machine (SVM) is a powerful and widely used classification algorithm. This paper uses the Karush-Kuhn-Tucker conditions to provide rigorous mathematical proof for new insights into behavior of SVM. These perhaps unexpected relationships between SVM two other linear classifiers: mean difference maximal data piling direction. For example, we show that in many cases can be viewe...

Geometric quantum gates are often expected to be more resilient than dynamical against certain types of error, which would make them ideal for robust computing. However, this is still up debate due seemingly conflicting results in the literature. Here we use invariant theory conjunction with filter functions order analytically characterize noise sensitivity an arbitrary gate. For any control Ha...

The notion of geometric construction is introduced. This notion allows to compare incidence configurations in the algebraic and tropical plane. We provide an algorithm such that, given a tropical instance of a geometric construction, it computes sufficient conditions to have an algebraic counterpart related by tropicalization. We also provide sufficient conditions in a geometric construction to...

Inspired by G. Frieden's recent work on the geometric R-matrix for affine type A crystal associated with rectangular shaped Young tableaux, we propose a method to construct novel family of discrete integrable systems which can be regarded as lifting generalized periodic box-ball systems. By converting conventional usage matrices defining Lax representation Toda chain, together clever use Perron...