In this paper we present a new family of minimal spectrally arbitrary patterns which allow for arbitrary spectrum by using the Nilpotent-Jacobian method introduced in [3]. The novel approach here is that we use the Intermediate Value Theorem to avoid finding an explicit nilpotent realization of the new minimal spectrally arbitrary patterns.

We illustrate an algorithm that starting from the image representation of a strictly bounded-real system computes a minimal balanced state variable, from which a minimal balanced state realization is readily obtained. The algorithm stems from an iterative procedure to compute a storage function, based on a technique to solve a generalization of the Nevanlinna interpolation problem.

We study D-branes in topologically twisted N = 2 minimal models using the Landau-Ginzburg realization. In the cases of A and D-type minimal models we provide what we believe is an exhaustive list of topological branes and compute the corresponding boundary OPE algebras as well as all disk correlators. We also construct examples of topological branes in E-type minimal models. We compare our resu...

We demonstrate that the minimal state space realization problem in the max algebra can be transformed into an Extended Linear Complementarity Problem (ELCP). We use an algorithm that finds all solutions of an ELCP to find all equivalent minimal state space realizations of a single input single output (SISO) discrete event system. We also give a geometrical description of the set of all minimal ...

The notion of realization for single-input single-output nonlinear systems is studied based on a new notion of input/output equivalence. This equivalence relation aims to generalize the equivalence of linear time-invarian t systems in the sense of the equality of their transfer functions. Necessary and suÆcient conditions are given for the existence of a realization, aÆne or not. A minimal (i.e...

We present realization theory for a class of autonomous discrete-time hybrid systems called semi-algebraic hybrid systems. These are systems in which the state and output equations associated with each discrete state are defined by polynomial equalities and inequalities. We first show that these systems generate the same output as semi-algebraic systems and implicit polynomial systems. We then ...

An optimal realization of a metric d on a set X is a weighted graph G = (V, E, w) such that X ⊆ V , dG(x, y) = d(x, y) for all x ∈ X, and ∑ e∈E w(e) is minimal. In this paper, we consider the conjecture that any finite metric (X, d) has some optimal realization obtainable as a subgraph of its tight span. For an extremal optimal realization G, defined as an optimal realizations for which the num...