Proof of the Dubrovin conjecture and analysis of the tritronqu\'ee solutions of PIP_I

We show that the tritronqu\'ee solution of the Painlev\'e equation $\P1$, $y"=6y^2+z$ which is analytic for large $z$ with $\arg z \in (-\frac{3\pi}{5}, \pi)$ is pole-free in a region containing the full sector ${z \ne 0, \arg z \in [-\frac{3\pi}{5}, \pi]}$ and the disk ${z: |z| < 37/20}$. This proves in particular the Dubrovin conjecture, an open problem in the theory of Painlev\'e transcendents. The method, building on a technique developed in Costin, Huang, Schlag (2012), is general and constructive. As a byproduct, we obtain the value of the tritronqu\'ee and its derivative at zero within less than 1/100 rigorous error bounds

A Semantic Collaboration Method Based on Uniform Knowledge Graph

The Semantic Internet of Things is the extension of the Internet of Things and the Semantic Web, which aims to build an interoperable collaborative system to solve the heterogeneous problems in the Internet of Things. However, the Semantic Internet of Things has the characteristics of both the Internet of Things and the Semantic Web environment, and the corresponding semantic data presents many new data features. In this study, we analyze the characteristics of semantic data and propose the concept of a uniform knowledge graph, allowing us to be applied to the environment of the Semantic Internet of Things better. Here, we design a semantic collaboration method based on a uniform knowledge graph. It can take the uniform knowledge graph as the form of knowledge organization and representation, and provide a useful data basis for semantic collaboration by constructing semantic links to complete semantic relation between different data sets, to achieve the semantic collaboration in the Semantic Internet of Things. Our experiments show that the proposed method can analyze and understand the semantics of user requirements better and provide more satisfactory outcomes

Actively Guided CanSats for Assisting Localization and Mapping in Unstructured and Unknown Environments

When navigating in unknown and unstructured environments, Unmanned Arial Vehicles (UAVs) can struggle when attempting to preform Simultaneous Localization and Mapping (SLAM) operations. Particularly challenging circumstance arise when an UAV may need to land or otherwise navigate through treacherous environments. As the primary UAV may be too large and unwieldly to safely investigate in these types of situations, this research effort proposes the use of actively guided CanSats for assisting in localization and mapping of unstructured environments. A complex UAV could carry multiple of these SLAM capable CanSats, and when additional mapping and localization capabilities where required, the CanSat would be ejected from the UAV to perform an unpowered but guided descent through the obstructed space. The CanSat\u27s sensors would then generate SLAM data, which would be concurrently communicated back to the primary UAV while also being used by the CanSat to navigate in the unknown environment. The successful mapping and navigation of the CanSat during descent could supply the UAV with adequate data to execute a more efficient and safe navigation across previously uncharted space. Potential uses of this technology include agricultural surveys, in which UAVs would launch SLAM capable CanSats to map the whole tree canopy of an orchard. Similar obstacles and opportunities may exist beyond Earth, with scientists becoming increasingly interested in the possibility for UAVs to serve as helpful pathfinders on distant planets. Many of the suggested scientific vehicles, however, will be too large and unwieldy to navigate in the narrow and enclosed regions that could be suitable for future manned habitats. The development of low-cost SLAM competent CanSats may therefore establish the technological foundation for enhanced sensory systems that could be deployed from large-scale interplanetary explorers to map unknown and unstructured environments on alien worlds

Intuitionistic Fuzzy Broad Learning System: Enhancing Robustness Against Noise and Outliers

In the realm of data classification, broad learning system (BLS) has proven to be a potent tool that utilizes a layer-by-layer feed-forward neural network. It consists of feature learning and enhancement segments, working together to extract intricate features from input data. The traditional BLS treats all samples as equally significant, which makes it less robust and less effective for real-world datasets with noises and outliers. To address this issue, we propose the fuzzy BLS (F-BLS) model, which assigns a fuzzy membership value to each training point to reduce the influence of noises and outliers. In assigning the membership value, the F-BLS model solely considers the distance from samples to the class center in the original feature space without incorporating the extent of non-belongingness to a class. We further propose a novel BLS based on intuitionistic fuzzy theory (IF-BLS). The proposed IF-BLS utilizes intuitionistic fuzzy numbers based on fuzzy membership and non-membership values to assign scores to training points in the high-dimensional feature space by using a kernel function. We evaluate the performance of proposed F-BLS and IF-BLS models on 44 UCI benchmark datasets across diverse domains. Furthermore, Gaussian noise is added to some UCI datasets to assess the robustness of the proposed F-BLS and IF-BLS models. Experimental results demonstrate superior generalization performance of the proposed F-BLS and IF-BLS models compared to baseline models, both with and without Gaussian noise. Additionally, we implement the proposed F-BLS and IF-BLS models on the Alzheimers Disease Neuroimaging Initiative (ADNI) dataset, and promising results showcase the models effectiveness in real-world applications. The proposed methods offer a promising solution to enhance the BLS frameworks ability to handle noise and outliers

Quantitative Susceptibility Mapping in Cognitive Decline: A Review of Technical Aspects and Applications

In the human brain, essential iron molecules for proper neurological functioning exist in transferrin (tf) and ferritin (Fe3) forms. However, its unusual increment manifests iron overload, which reacts with hydrogen peroxide. This reaction will generate hydroxyl radicals, and irons higher oxidation states. Further, this reaction causes tissue damage or cognitive decline in the brain and also leads to neurodegenerative diseases. The susceptibility difference due to iron overload within the volume of interest (VOI) responsible for field perturbation of MRI and can benefit in estimating the neural disorder. The quantitative susceptibility mapping (QSM) technique can estimate susceptibility alteration and assist in quantifying the local tissue susceptibility differences. It has attracted many researchers and clinicians to diagnose and detect neural disorders such as Parkinsons, Alzheimers, Multiple Sclerosis, and aging. The paper presents a systematic review illustrating QSM fundamentals and its processing steps, including phase unwrapping, background field removal, and susceptibility inversion. Using QSM, the present work delivers novel predictive biomarkers for various neural disorders. It can strengthen new researchers fundamental knowledge and provides insight into its applicability for cognitive decline disclosure. The paper discusses the future scope of QSM processing stages and their applications in identifying new biomarkers for neural disorders

RoBoSS: A Robust, Bounded, Sparse, and Smooth Loss Function for Supervised Learning

In the domain of machine learning algorithms, the significance of the loss function is paramount, especially in supervised learning tasks. It serves as a fundamental pillar that profoundly influences the behavior and efficacy of supervised learning algorithms. Traditional loss functions, while widely used, often struggle to handle noisy and high-dimensional data, impede model interpretability, and lead to slow convergence during training. In this paper, we address the aforementioned constraints by proposing a novel robust, bounded, sparse, and smooth (RoBoSS) loss function for supervised learning. Further, we incorporate the RoBoSS loss function within the framework of support vector machine (SVM) and introduce a new robust algorithm named $\mathcal{L}_{rbss}$-SVM. For the theoretical analysis, the classification-calibrated property and generalization ability are also presented. These investigations are crucial for gaining deeper insights into the performance of the RoBoSS loss function in the classification tasks and its potential to generalize well to unseen data. To empirically demonstrate the effectiveness of the proposed $\mathcal{L}_{rbss}$-SVM, we evaluate it on $88$ real-world UCI and KEEL datasets from diverse domains. Additionally, to exemplify the effectiveness of the proposed $\mathcal{L}_{rbss}$-SVM within the biomedical realm, we evaluated it on two medical datasets: the electroencephalogram (EEG) signal dataset and the breast cancer (BreaKHis) dataset. The numerical results substantiate the superiority of the proposed $\mathcal{L}_{rbss}$-SVM model, both in terms of its remarkable generalization performance and its efficiency in training time