Abstract Machine learning on trees has been mostly focused as input. Much less research investigated output, which many applications, such molecule optimization for drug discovery, or hint generation intelligent tutoring systems. In this work, we propose a novel autoencoder approach, called recursive tree grammar (RTG-AE), encodes via bottom-up parser and decodes grammar, both learned neural ne...

In this paper, based on feedback linearization control method and using a special PI (propotational integrator) regulator (IP) in combination with a feed-forward controller, a three-phase induction servo-drive is speed controlled. First, an observer is employed to estimate the rotor d and q axis flux components. Then, two input-output state variables are introduced to control the dynamics of to...

In this paper, a comparison among the hybrid of Fourier Transform and AdomianDecomposition Method (FTADM) and Homotopy Perturbation Method (HPM) is investigated.The linear and non-linear Newell-Whitehead-Segel (NWS) equations are solved and the results arecompared with the exact solution. The comparison reveals that for the same number of componentsof recursive sequences, the error of FTADM is ...

A Space Free-Flying Robot (SFFR) includes an actuated base equipped with one or more manipulators to perform on-orbit missions. Distinct from fixed-based manipulators, the spacecraft (base) of a SFFR responds to dynamic reaction forces due to manipulator motions. In order to control such a system, it is essential to consider the dynamic coupling between the manipulators and the base. Explicit d...

A recursive graph is a graph whose vertex and edges sets are recursive. A highly recursive graph is a recursive graph that also has the following property: one can recursively determine the neighbors of a vertex. Both of these have been studied in the literature. We consider an intermediary notion: Let A be a set. An Arecursive graph is a recursive graph that also has the following property: on...

In this article we revisit the approach by Bove and Capretta for formulating partial recursive functions in Martin-Löf Type Theory by indexed inductive-recursive definitions. We will show that all inductiverecursive definitions used there can be replaced by inductive definitions. However, this encoding results in an additional technical overhead. In order to obtain directly executable partial r...

We investigate the complexity of finding solutions to infinite recursive constraint satisfaction problems. We show that, in general, the problem of finding a solution to an infinite recursive constraint satisfaction problem is equivalent to the problem of finding an infinite path through a recursive tree. We also identify natural classes of infinite recursive constraint problems where the probl...

If $G$ is a connected graph with vertex set $V$, then the eccentric connectivity index of $G$, $xi^c(G)$, is defined as $sum_{vin V(G)}deg(v)ecc(v)$ where $deg(v)$ is the degree of a vertex $v$ and $ecc(v)$ is its eccentricity. In this paper we show some convergence in probability and an asymptotic normality based on this index in random bucket recursive trees.

Where mutually recursive data types are used in programming languages, etc., mutually recursive functions are usually required. Mutually recursive functions are also quite common for non-mutually recursive types. Reasoning about recursive functions requires some form of mathematical induction but there have been difficulties in adapting induction methods for simple recursion to the mutually rec...