Two Extensions of Cover Automata

Deterministic Finite Cover Automata (DFCA) are compact representations of finite languages. Deterministic Finite Automata with “do not care” symbols and Multiple Entry Deterministic Finite Automata are both compact representations of regular languages. This paper studies the benefits of combining these representations to get even more compact representations of finite languages. DFCAs are extended by accepting either “do not care” symbols or considering multiple entry DFCAs. We study for each of the two models the existence of the minimization or simplification algorithms and their computational complexity, the state complexity of these representations compared with other representations of the same language, and the bounds for state complexity in case we perform a representation transformation. Minimization for both models proves to be NP-hard. A method is presented to transform minimization algorithms for deterministic automata into simplification algorithms applicable to these extended models. DFCAs with “do not care” symbols prove to have comparable state complexity as Nondeterministic Finite Cover Automata. Furthermore, for multiple entry DFCAs, we can have a tight estimate of the state complexity of the transformation into equivalent DFCA.

Nauyaca: a New Tool to Determine Planetary Masses and Orbital Elements through Transit Timing Analysis

The transit timing variations method is currently the most successful method to determine dynamical masses and orbital elements for Earth-sized transiting planets. Precise mass determination is fundamental to restrict planetary densities and thus infer planetary compositions. In this work, we present Nauyaca, a Python package dedicated to finding planetary masses and orbital elements through the fitting of observed midtransit times from an N-body approach. The fitting strategy consists of performing a sequence of minimization algorithms (optimizers) that are used to identify high probability regions in the parameter space. These results from optimizers are used for initialization of a Markov chain Monte Carlo method, using an adaptive Parallel-Tempering algorithm. A set of runs are performed in order to obtain posterior distributions of planetary masses and orbital elements. In order to test the tool, we created a mock catalog of synthetic planetary systems with different numbers of planets where all of them transit. We calculate their midtransit times to give them as an input to Nauyaca, testing statistically its efficiency in recovering the planetary parameters from the catalog. For the recovered planets, we find typical dispersions around the real values of ∼1–14 M ⊕ for masses, between 10–110 s for periods, and between ∼0.01–0.03 for eccentricities. We also investigate the effects of the signal-to-noise ratio and number of transits on the correct determination of the planetary parameters. Finally, we suggest choices of the parameters that govern the tool for the usage with real planets, according to the complexity of the problem and computational facilities.

Design of Constraints for Seeking Maximum Torque per Ampere Techniques in an Interior Permanent Magnet Synchronous Motor Control

The efficient control of permanent magnet synchronous motors (PMSM) requires the development of a technique for loss optimization. The best approach is the implementation of power loss minimization algorithms, which are hard to model and design. Therefore, the developers typically involve maximum torque per ampere (MTPA) control, which optimizes Joule loss only. The conventional MTPA control requires knowledge of motor parameters and can only properly operate when these parameters are constant. However, motor parameters vary depending on operating conditions; thus, conventional techniques cannot be used. Furthermore, many industrial drives are designed for self-commissioning, and they do not have prior information on motor parameters. In order to solve this problem, various MTPA-seeking techniques, which track the minimum of motor current, have been developed. The dynamic performance between these seeking algorithms and maximum deviation from the true MTPA trajectory are defined by the constraints in most cases, in which proper design improves the dynamic behavior of MTPA-seeking algorithms. This paper considers a PMSM, which was designed to operate in the saturation area and whose MTPA trajectory significantly deviates from the same curve constructed for the initial unsaturated parameters. This paper considers existing approaches, explains their pros and cons, and demonstrates that these methods do not utilize full potential of the motor. A new constraint design was proposed and explained step by step. The experiment verifies the proposed technique and demonstrates improvements in efficiency and dynamic behavior of the seeking algorithm.

Optimization of 3D printed porous materials accounting for manufacturing defects

Open-cell materials are well-known for their low price, low weight, and broadband acoustic behavior. They form one of the most used class of acoustic treatments but suffer from a lack of versatility when made by conventional manufacturing processes. Recent advances in additive manufacturing allow to produce porous materials having a controlled microstructure. In this way, the design of treatments including porous materials is not limited to a catalog of existing media. The macroscopic behavior is governed by the micro-geometry of the porous medium, which can be estimated by numerical models. Then, acoustic treatments can be optimized numerically using predicting models and minimization algorithms. However, additive manufacturing induces defects often too complex to be accounted for numerically. In this presentation, a method allowing to obtain the parametric model of the intrinsic behavior of a 3D-printed porous material is presented. The corrected model is used in the optimization of several porous treatments; namely, graded porous materials, folded porous materials and metaporous surfaces. These treatments are versatile and display remarkable properties. They provide quasi-perfect absorption at several frequencies that can be out of reach of standard porous treatments in normal or oblique incidence. Experimental validations confirm the relevance of the proposed design processes.

A minimization algorithm for fuzzy top-down tree automata over lattices

In this paper, we study fuzzy top-down tree automata over lattices ( LTA s , for short). The purpose of this contribution is to investigate the minimization problem for LTA s . We first define the concept of statewise equivalence between two LTA s . Thereafter, we show the existence of the statewise minimal form for an LTA . To this end, we find a statewise irreducible LTA which is equivalent to a given LTA . Then, we provide an algorithm to find the statewise minimal LTA and by a theorem, we show that the output statewise minimal LTA is statewise equivalent to the given input. Moreover, we compute the time complexity of the given algorithm. The proposed algorithm can be applied to any given LTA and, unlike some minimization algorithms given in the literature, the input doesn’t need to be a complete, deterministic, or reduced lattice-valued tree automaton. Finally, we provide some examples to show the efficiency of the presented algorithm.