The local disturbance decoupling problem with stability for nonlinear systems

In this paper the Disturbance Decoupling Problem with Stability (DDPS) for nonlinear systems is considered. The DDPS is the problem of finding a feedback such that after applying this feedback the disturbances do not influence the output anymore and x = 0 is an exponentially stable equilibrium point of the feedback system. For systems that can be decoupled by static state feedback it is possible to define (under fairly mild assumptions) a distribution Δs* which is the nonlinear analogue of the linear V*s, the largest stabilizable controlled invariant subspace in the kernel of the output mapping, and to prove that the DDPS is locally solvable if and only if the disturbance vector fields are contained in Δs*

Stable gonality is computable

Stable gonality is a multigraph parameter that measures the complexity of a graph. It is defined using maps to trees. Those maps, in some sense, divide the edges equally over the edges of the tree; stable gonality asks for the map with the minimum number of edges mapped to each edge of the tree. This parameter is related to treewidth, but unlike treewidth, it distinguishes multigraphs from their underlying simple graphs. Stable gonality is relevant for problems in number theory. In this paper, we show that deciding whether the stable gonality of a given graph is at most a given integer $k$ belongs to the class NP, and we give an algorithm that computes the stable gonality of a graph in $O((1.33n)^nm^m \text{poly}(n,m))$ time.Comment: 15 pages; v2 minor changes; v3 minor change

Computing graph gonality is hard

There are several notions of gonality for graphs. The divisorial gonality dgon(G) of a graph G is the smallest degree of a divisor of positive rank in the sense of Baker-Norine. The stable gonality sgon(G) of a graph G is the minimum degree of a finite harmonic morphism from a refinement of G to a tree, as defined by Cornelissen, Kato and Kool. We show that computing dgon(G) and sgon(G) are NP-hard by a reduction from the maximum independent set problem and the vertex cover problem, respectively. Both constructions show that computing gonality is moreover APX-hard.Comment: The previous version only dealt with hardness of the divisorial gonality. The current version also shows hardness of stable gonality and discusses the relation between the two graph parameter

Minimality of dynamic input-output decoupling for nonlinear systems

In this note we study the strong dynamic input-output decoupling problem for nonlinear systems. Using an algebraic theory for nonlinear control systems, we obtain for a dynamic input-output decouplable nonlinear system a compensator of minimal dimension that solves the decoupling problem

Gene Therapy of Liver Disease with Lentiviral Vectors Preclinical Studies in Models of Crigler-Najjar Disease and Hepatitis C

The main theme of this thesis is the application of lentiviral vectors for the treatment of congenital and acquired liver disease. Gene therapy represents a relatively new and promising therapeutic tool with possible applications in a broad spectrum of medical disciplines. The underlying principle of gene therapy is based on the introduction of genetic material into living cells to achieve a therapeutic biological effect. Consequently, gene therapy focuses on treating the cause of disease rather than the symptoms. The first part of this introduction will review the current options and developments in the field of liver directed gene therapy (1.1). Next we will review the most widely used viral vector systems (1.2). HIV-1 derived lentiviral vectors are among the most efficient gene therapy vectors that are currently available. The capacity of lentiviral vectors to stably integrate into the target cell genome of non-dividing cells is one of the main distinguishing features of this vector system. Clinical trials that involve the ex vivo transduction and retransplantation of autologous CD4+ T-cells or hematopoietic stem cells have been initiated [1-3]. In preclinical experiments, lentiviral vectors efficiently transduce differentiated liver parenchymal cells in vivo [4, 5]. Other major targets, such as the central nervous system and the airways are also under intense investigation [6, 7]. In the third part of this introduction, we will introduce