Learning Preconditioner for Conjugate Gradient PDE Solvers

Efficient numerical solvers for partial differential equations empower science and engineering. One of the commonly employed numerical solvers is the preconditioned conjugate gradient (PCG) algorithm which can solve large systems to a given precision level. One challenge in PCG solvers is the selection of preconditioners, as different problem-dependent systems can benefit from different preconditioners. We present a new method to introduce \emph{inductive bias} in preconditioning conjugate gradient algorithm. Given a system matrix and a set of solution vectors arise from an underlying distribution, we train a graph neural network to obtain an approximate decomposition to the system matrix to be used as a preconditioner in the context of PCG solvers. We conduct extensive experiments to demonstrate the efficacy and generalizability of our proposed approach in solving various 2D and 3D linear second-order PDEs

Dynamic spatial segmentation strategy based magnetic field indoor positioning system

In this day and age, it is imperative for anyone who relies on a mobile device to track and navigate themselves using the Global Positioning System (GPS). Such satellite-based positioning works as intended when in the outdoors, or when the device is able to have unobstructed communication with GPS satellites. Nevertheless, at the same time, GPS signal fades away in indoor environments due to the effects of multi-path components and obstructed line-of-sight to the satellite. Therefore, numerous indoor localisation applications have emerged in the market, geared towards finding a practical solution to satisfy the need for accuracy and efficiency. The case of Indoor Positioning System (IPS) is promoted by recent smart devices, which have evolved into a multimedia device with various sensors and optimised connectivity. By sensing the device’s surroundings and inferring its context, current IPS technology has proven its ability to provide stable and reliable indoor localisation information. However, such a system is usually dependent on a high-density of infrastructure that requires expensive installations (e.g. Wi-Fi-based IPS). To make a trade-off between accuracy and cost, considerable attention from many researchers has been paid to the range of infrastructure-free technologies, particularly exploiting the earth’s magnetic field (EMF). EMF is a promising signal type that features ubiquitous availability, location specificity and long-term stability. When considering the practicality of this typical signal in IPS, such a system only consists of mobile device and the EMF signal. To fully comprehend the conventional EMF-based IPS reported in the literature, a preliminary experimental study on indoor EMF characteristics was carried out at the beginning of this research. The results revealed that the positioning performance decreased when the presence of magnetic disturbance sources was lowered to a minimum. In response to this finding, a new concept of spatial segmentation is devised in this research based on magnetic anomaly (MA). Therefore, this study focuses on developing innovative techniques based on spatial segmentation strategy and machine learning algorithms for effective indoor localisation using EMF. In this thesis, four closely correlated components in the proposed system are included: (i) Kriging interpolation-based fingerprinting map; (ii) magnetic intensity-based spatial segmentation; (iii) weighted Naïve Bayes classification (WNBC); (iv) fused features-based k-Nearest-Neighbours (kNN) algorithm. Kriging interpolation-based fingerprinting map reconstructs the original observed EMF positioning database in the calibration phase by interpolating predicted points. The magnetic intensity-based spatial segmentation component then investigates the variation tendency of ambient EMF signals in the new database to analyse the distribution of magnetic disturbance sources, and accordingly, segmenting the test site. Then, WNBC blends the exclusive characteristics of indoor EMF into original Naïve Bayes Classification (NBC) to enable a more accurate and efficient segmentation approach. It is well known that the best IPS implementation often exerts the use of multiple positing sources in order to maximise accuracy. The fused features-based kNN component used in the positioning phase finally learns the various parameters collected in the calibration phase, continuously improving the positioning accuracy of the system. The proposed system was evaluated on multiple indoor sites with diverse layouts. The results show that it outperforms state-of-the-art approaches and demonstrate an average accuracy between 1-2 meters achieved in typical sites by the best methods proposed in this thesis across most of the experimental environments. It can be believed that such an accurate approach will enable the future of infrastructure–free IPS technologies

Dynamic RACH Partition for Massive Access of Differentiated M2M Services

In machine-to-machine (M2M) networks, a key challenge is to overcome the overload problem caused by random access requests from massive machine-type communication (MTC) devices. When differentiated services coexist, such as delay-sensitive and delay-tolerant services, the problem becomes more complicated and challenging. This is because delay-sensitive services often use more aggressive policies, and thus, delay-tolerant services get much fewer chances to access the network. To conquer the problem, we propose an efficient mechanism for massive access control over differentiated M2M services, including delay-sensitive and delay-tolerant services. Specifically, based on the traffic loads of the two types of services, the proposed scheme dynamically partitions and allocates the random access channel (RACH) resource to each type of services. The RACH partition strategy is thoroughly optimized to increase the access performances of M2M networks. Analyses and simulation demonstrate the effectiveness of our design. The proposed scheme can outperform the baseline access class barring (ACB) scheme, which ignores service types in access control, in terms of access success probability and the average access delay

On Uni-Modal Feature Learning in Supervised Multi-Modal Learning

We abstract the features (i.e. learned representations) of multi-modal data into 1) uni-modal features, which can be learned from uni-modal training, and 2) paired features, which can only be learned from cross-modal interactions. Multi-modal models are expected to benefit from cross-modal interactions on the basis of ensuring uni-modal feature learning. However, recent supervised multi-modal late-fusion training approaches still suffer from insufficient learning of uni-modal features on each modality. We prove that this phenomenon does hurt the model's generalization ability. To this end, we propose to choose a targeted late-fusion learning method for the given supervised multi-modal task from Uni-Modal Ensemble(UME) and the proposed Uni-Modal Teacher(UMT), according to the distribution of uni-modal and paired features. We demonstrate that, under a simple guiding strategy, we can achieve comparable results to other complex late-fusion or intermediate-fusion methods on various multi-modal datasets, including VGG-Sound, Kinetics-400, UCF101, and ModelNet40

Packing Densities of Delzant and Semitoric Polygons

Exploiting the relationship between 4-dimensional toric and semitoric integrable systems with Delzant and semitoric polygons, respectively, we develop techniques to compute certain equivariant packing densities and equivariant capacities of these systems by working exclusively with the polygons. This expands on results of Pelayo and Pelayo-Schmidt. We compute the densities of several important examples and we also use our techniques to solve the equivariant semitoric perfect packing problem, i.e., we list all semitoric polygons for which the associated semitoric system admits an equivariant packing which fills all but a set of measure zero of the manifold. This paper also serves as a concise and accessible introduction to Delzant and semitoric polygons in dimension four

Survival and Environmental Stress Resistance of Cronobacter sakazakii Exposed to Vacuum or Air Packaging and Stored at Different Temperatures

The aim of this study was to evaluate the survival of Cronobacter sakazakii exposed to vacuum or air packaging, then stored at 4, 10, or 25°C, and the environmental stress resistance of vacuum-packaged or air-packaged bacterial cells were determined by subjecting the cells to reconstituted infant formula at 50°C, in acid (simulated gastric fluid, pH = 3.5), and in bile salt [bile salt solution, 5% (wt/vol)]. A cocktail culture of C. sakazakii desiccated on the bottom of sterile petri plates was air-packaged or vacuum-packaged and then stored at 4, 10, or 25°C for 10 days. The viable cell populations during storage were examined, and the vacuum-packaged and air-packaged cells (stored at 10°C for 4 days) were subsequently exposed to heat, acid, or bile salt. The results show that the populations of vacuum-packaged and air-packaged C. sakazakii were reduced by 1.6 and 0.9 log colony-forming units (CFU)/ml at 4°C and by 1.6 and 1.3 log CFU/ml at 25°C, respectively, in 10 days. At 10°C, significant reductions of 3.1 and 2.4 log CFU/ml were observed for vacuum-packaged and air-packaged cells, respectively. Vacuum packaging followed by storage at 10°C for 4 days caused significant decreases in the resistance of C. sakazakii to heat, acid, and bile salt conditions compared with air packaging. These results suggest that the application of vacuum packaging for powdered infant formula could be useful to minimize the risk of C. sakazakii