Automatic sets of rational numbers

The notion of a k-automatic set of integers is well-studied. We develop a new notion - the k-automatic set of rational numbers - and prove basic properties of these sets, including closure properties and decidability.Comment: Previous version appeared in Proc. LATA 2012 conferenc

Modelling the air-gap field strength of electric machines to improve performance of haptic mechanisms

The air-gap of electro-magnetic (EM) actuators determines key operating parameters such as their ability to generate force. In haptic devices these parameters are not optimised for the conditions typically seen in operation and include the heat produced in the air-gap, the volume of the air-gap, and the intensity and direction of the magnetic field. The relationship between these parameters is complex thus design decisions are difficult to make. This paper considers the role of the radial magnetic field in cylindrical electric motors, a type often used in haptic devices. Two models are derived and compared with experimental measurements. The first model is a closed form solution, the second is a classic Poisson solution to Ampere's equation. These models are shown to be valid for making more general design decisions in relation to haptic actuators, and in particular allow an evaluation of the trade off between the volume of the air-gap, the resulting radial magnetic field and hence heat generated and the resulting forces

Effects of stator and rotor core ovality on induction machine behavior

Asymmetries in the air gap of induction motors produce additional harmonics in the flux density and force waves. A complete transient finite element model analyzes the harmonics produced from two possible asymmetries, a stator core ovality and a rotor ovality. The analysis of the air gap flux density and magnetic force waves determined by the finite element model shows unique harmonic frequencies due to the ovality of the air gap

Computing the External Magnetic Scalar Potential due to an Unbalanced Six-Pole Permanent Magnet Motor

The accurate computation of the external magnetic field from a permanent magnet motor is accomplished by first computing its magnetic scalar potential. In order to find a solution which is valid for any arbitrary point external to the motor, a number of proven methods have been employed. Firstly, A finite element model is developed which helps generate magnetic scalar potential values valid for points close to and outside the motor. Secondly, charge simulation is employed which generates an equivalent magnetic charge matrix. Finally, an equivalent multipole expansion is developed through the application of a toroidal harmonic expansion. This expansion yields the harmonic components of the external magnetic scalar potential which can be used to compute the magnetic field at any point outside the motor

Nanocomposites with functionalised polysaccharide nanocrystals through aqueous free radical polymerisation promoted by ozonolysis

Cellulose nanocrystals (CNC) and starch nanocrystals (SNC) were grafted by ozone-initiated free-radical polymerisation of styrene in a heterogeneous medium. Surface functionalisation was confirmed by infrared spectroscopy, contact angle measurements, and thermogravimetric and elemental analysis. X-ray diffraction and scanning electron microscopy showed that there was no significant change in the morphology or crystallinity of the nanoparticles following ozonolysis. The grafting efficiency, quantified by 13C NMR, was greater for SNC, with a styrene/anhydroglucose ratio of 1.56 compared to 0.25 for CNC. The thermal stability improved by 100 °C. The contact angles were 97° and 78° following the SNC and CNC grafting, respectively, demonstrating the efficiency of the grafting in changing the surface properties even at low levels of surface substitution. The grafting increased the compatibility with the polylactide, and produced nanocomposites with improved water vapour barrier properties. Ozone-mediated grafting is thus a promising approach for surface functionalisation of polysaccharide nanocrystals

Using machine learning and Biogeochemical-Argo (BGC-Argo) floats to assess biogeochemical models and optimize observing system design

Numerical models of ocean biogeochemistry are becoming the major tools used to detect and predict the impact of climate change on marine resources and to monitor ocean health. However, with the continuous improvement of model structure and spatial resolution, incorporation of these additional degrees of freedom into fidelity assessment has become increasingly challenging. Here, we propose a new method to provide information on the model predictive skill in a concise way. The method is based on the conjoint use of a k-means clustering technique, assessment metrics, and Biogeochemical-Argo (BGC-Argo) observations. The k-means algorithm and the assessment metrics reduce the number of model data points to be evaluated. The metrics evaluate either the model state accuracy or the skill of the model with respect to capturing emergent properties, such as the deep chlorophyll maximums and oxygen minimum zones. The use of BGC-Argo observations as the sole evaluation data set ensures the accuracy of the data, as it is a homogenous data set with strict sampling methodologies and data quality control procedures. The method is applied to the Global Ocean Biogeochemistry Analysis and Forecast system of the Copernicus Marine Service. The model performance is evaluated using the model efficiency statistical score, which compares the model–observation misfit with the variability in the observations and, thus, objectively quantifies whether the model outperforms the BGC-Argo climatology. We show that, overall, the model surpasses the BGC-Argo climatology in predicting pH, dissolved inorganic carbon, alkalinity, oxygen, nitrate, and phosphate in the mesopelagic and the mixed layers as well as silicate in the mesopelagic layer. However, there are still areas for improvement with respect to reducing the model–data misfit for certain variables such as silicate, pH, and the partial pressure of CO2 in the mixed layer as well as chlorophyll-a-related, oxygen-minimum-zone-related, and particulate-organic-carbon-related metrics. The method proposed here can also aid in refining the design of the BGC-Argo network, in particular regarding the regions in which BGC-Argo observations should be enhanced to improve the model accuracy via the assimilation of BGC-Argo data or process-oriented assessment studies. We strongly recommend increasing the number of observations in the Arctic region while maintaining the existing high-density of observations in the Southern Oceans. The model error in these regions is only slightly less than the variability observed in BGC-Argo measurements. Our study illustrates how the synergic use of modeling and BGC-Argo data can both provide information about the performance of models and improve the design of observing systems.</p

Activity Dependent Protein Degradation Is Critical for the Formation and Stability of Fear Memory in the Amygdala

Protein degradation through the ubiquitin-proteasome system [UPS] plays a critical role in some forms of synaptic plasticity. However, its role in memory formation in the amygdala, a site critical for the formation of fear memories, currently remains unknown. Here we provide the first evidence that protein degradation through the UPS is critically engaged at amygdala synapses during memory formation and retrieval. Fear conditioning results in NMDA-dependent increases in degradation-specific polyubiquitination in the amygdala, targeting proteins involved in translational control and synaptic structure and blocking the degradation of these proteins significantly impairs long-term memory. Furthermore, retrieval of fear memory results in a second wave of NMDA-dependent polyubiquitination that targets proteins involved in translational silencing and synaptic structure and is critical for memory updating following recall. These results indicate that UPS-mediated protein degradation is a major regulator of synaptic plasticity necessary for the formation and stability of long-term memories at amygdala synapses