We investigate optimal control of dynamical systems which are affine, i.e., linear in control, but nonlinear in state. The control task is to enforce the system state to follow a prescribed desired trajectory as closely as possible, a task also known as optimal trajectory tracking. To obtain wellbehaved solutions to optimal control, a regularization term with coefficient ε must be included in t...

We study Jacobi structures on the dual bundle A to a vector bundle A such that the Jacobi bracket of linear functions is again linear and the Jacobi bracket of a linear function and the constant function 1 is a basic function. We prove that a Lie algebroid structure on A and a 1-cocycle φ ∈ Γ(A) induce a Jacobi structure on A satisfying the above conditions. Moreover, we show that this correspo...

A dilatation structure on a metric space, introduced in [3], is a notion in between a group and a differential structure, accounting for the approximate self-similarity of the metric space. The basic objects of a dilatation structure are dilatations (or contractions). The axioms of a dilatation structure set the rules of interaction between different dilatations. A metric space (X, d) which adm...

We present Linear Relational Embedding (LRE), a new method of learning a distributed representation of concepts from data consisting of instances of relations between given concepts. Its final goal is to be able to generalize, i.e. infer new instances of these relations among the concepts. On a task involving family relationships we show that LRE can generalize better than any previously publis...

Many observed spatial point patterns contain points placed roughly on line segments. Point patterns exhibiting such structures can be found for example in archaeology (locations of bronze age graves in Denmark) and geography (locations of mountain tops). We consider a particular class of point processes whose realizations contain such linear structures. Such a point process is constructed seque...

Early tests of short low group velocity and standing wave structures indicated the viability of operating Xband linacs with accelerating gradients in excess of 100 MeV/m. Conventional scaling of traveling wave traveling wave linacs with frequency scales the cell dimensions with λ. Because Q scales as λ, the length of the structures scale not linearly but as λ in order to preserve the attenuatio...

The classical pattern matching paradigm is that of seeking occurrences of one string in another, where both strings are drawn from an alphabet set Σ. In the parameterized pattern matching model, a consistent renaming of symbols from Σ is allowed in a match. The parameterized matching paradigm has proven useful in problems in software engineering, computer vision, and other applications. In clas...

A modification of a classical Vector Linear Prediction (VLP) technique is proposed in this paper, enabling significant reduction in complexity. The proposed sparse VLP technique (sVLP) is based on predictors with reduced number of nonzero elements. For a given input vector process, a design procedure for obtaining optimal sparse predictor structures and matrix elements is described. The effecti...

A dilatation structure on a metric space, is a notion in between a group and a differential structure. The basic objects of a dilatation structure are dilatations (or contractions). The axioms of a dilatation structure set the rules of interaction between different dilatations. There are two notions of linearity associated to dilatation structures: the linearity of a function between two dilata...

We introduce a Game Semantics where strategies are partial orders, and composition is a generalization of the merging of orders. Building on this, to bridge between Game Semantics and Concurrency, we explore the relation between Event Structures and Linear Strategies. The former are a true concurrency model introduced by Nielsen, Plotkin, Winskel, the latter a family of linear innocent strategi...