Hydrodynamic Flows on Curved Surfaces: Spectral Numerical Methods for Radial Manifold Shapes

We formulate hydrodynamic equations and spectrally accurate numerical methods for investigating the role of geometry in flows within two-dimensional fluid interfaces. To achieve numerical approximations having high precision and level of symmetry for radial manifold shapes, we develop spectral Galerkin methods based on hyperinterpolation with Lebedev quadratures for $L^2$-projection to spherical harmonics. We demonstrate our methods by investigating hydrodynamic responses as the surface geometry is varied. Relative to the case of a sphere, we find significant changes can occur in the observed hydrodynamic flow responses as exhibited by quantitative and topological transitions in the structure of the flow. We present numerical results based on the Rayleigh-Dissipation principle to gain further insights into these flow responses. We investigate the roles played by the geometry especially concerning the positive and negative Gaussian curvature of the interface. We provide general approaches for taking geometric effects into account for investigations of hydrodynamic phenomena within curved fluid interfaces.Comment: 14 figure

Novel neural approaches to data topology analysis and telemedicine

1noL'abstract è presente nell'allegato / the abstract is in the attachmentopen676. INGEGNERIA ELETTRICAnoopenRandazzo, Vincenz

Online Spectral Clustering on Network Streams

Graph is an extremely useful representation of a wide variety of practical systems in data analysis. Recently, with the fast accumulation of stream data from various type of networks, significant research interests have arisen on spectral clustering for network streams (or evolving networks). Compared with the general spectral clustering problem, the data analysis of this new type of problems may have additional requirements, such as short processing time, scalability in distributed computing environments, and temporal variation tracking. However, to design a spectral clustering method to satisfy these requirements certainly presents non-trivial efforts. There are three major challenges for the new algorithm design. The first challenge is online clustering computation. Most of the existing spectral methods on evolving networks are off-line methods, using standard eigensystem solvers such as the Lanczos method. It needs to recompute solutions from scratch at each time point. The second challenge is the parallelization of algorithms. To parallelize such algorithms is non-trivial since standard eigen solvers are iterative algorithms and the number of iterations can not be predetermined. The third challenge is the very limited existing work. In addition, there exists multiple limitations in the existing method, such as computational inefficiency on large similarity changes, the lack of sound theoretical basis, and the lack of effective way to handle accumulated approximate errors and large data variations over time. In this thesis, we proposed a new online spectral graph clustering approach with a family of three novel spectrum approximation algorithms. Our algorithms incrementally update the eigenpairs in an online manner to improve the computational performance. Our approaches outperformed the existing method in computational efficiency and scalability while retaining competitive or even better clustering accuracy. We derived our spectrum approximation techniques GEPT and EEPT through formal theoretical analysis. The well established matrix perturbation theory forms a solid theoretic foundation for our online clustering method. We facilitated our clustering method with a new metric to track accumulated approximation errors and measure the short-term temporal variation. The metric not only provides a balance between computational efficiency and clustering accuracy, but also offers a useful tool to adapt the online algorithm to the condition of unexpected drastic noise. In addition, we discussed our preliminary work on approximate graph mining with evolutionary process, non-stationary Bayesian Network structure learning from non-stationary time series data, and Bayesian Network structure learning with text priors imposed by non-parametric hierarchical topic modeling

Exploratory Cluster Analysis from Ubiquitous Data Streams using Self-Organizing Maps

This thesis addresses the use of Self-Organizing Maps (SOM) for exploratory cluster analysis over ubiquitous data streams, where two complementary problems arise: first, to generate (local) SOM models over potentially unbounded multi-dimensional non-stationary data streams; second, to extrapolate these capabilities to ubiquitous environments. Towards this problematic, original contributions are made in terms of algorithms and methodologies. Two different methods are proposed regarding the first problem. By focusing on visual knowledge discovery, these methods fill an existing gap in the panorama of current methods for cluster analysis over data streams. Moreover, the original SOM capabilities in performing both clustering of observations and features are transposed to data streams, characterizing these contributions as versatile compared to existing methods, which target an individual clustering problem. Also, additional methodologies that tackle the ubiquitous aspect of data streams are proposed in respect to the second problem, allowing distributed and collaborative learning strategies. Experimental evaluations attest the effectiveness of the proposed methods and realworld applications are exemplified, namely regarding electric consumption data, air quality monitoring networks and financial data, motivating their practical use. This research study is the first to clearly address the use of the SOM towards ubiquitous data streams and opens several other research opportunities in the future

Granular-ball computing: an efficient, robust, and interpretable adaptive multi-granularity representation and computation method

Human cognition operates on a "Global-first" cognitive mechanism, prioritizing information processing based on coarse-grained details. This mechanism inherently possesses an adaptive multi-granularity description capacity, resulting in computational traits such as efficiency, robustness, and interpretability. The analysis pattern reliance on the finest granularity and single-granularity makes most existing computational methods less efficient, robust, and interpretable, which is an important reason for the current lack of interpretability in neural networks. Multi-granularity granular-ball computing employs granular-balls of varying sizes to daptively represent and envelop the sample space, facilitating learning based on these granular-balls. Given that the number of coarse-grained "granular-balls" is fewer than sample points, granular-ball computing proves more efficient. Moreover, the inherent coarse-grained nature of granular-balls reduces susceptibility to fine-grained sample disturbances, enhancing robustness. The multi-granularity construct of granular-balls generates topological structures and coarse-grained descriptions, naturally augmenting interpretability. Granular-ball computing has successfully ventured into diverse AI domains, fostering the development of innovative theoretical methods, including granular-ball classifiers, clustering techniques, neural networks, rough sets, and evolutionary computing. This has notably ameliorated the efficiency, noise robustness, and interpretability of traditional methods. Overall, granular-ball computing is a rare and innovative theoretical approach in AI that can adaptively and simultaneously enhance efficiency, robustness, and interpretability. This article delves into the main application landscapes for granular-ball computing, aiming to equip future researchers with references and insights to refine and expand this promising theory

Dynamic Content-based Indexing in Mobile edge Networks

Recently, we have seen a huge growth in the usage of mobile devices, and with this growth, the data generated has also increased, being in a huge scale, user generated, e.g, photos, books, texts or messages/e-mails. Usually this data requires a permanent storage and its respective indexing for users to efficiently access it however, due to the unpredictability of this data, a concern regarding its indexing starts to raise as it can be hard to predict labels and indexes capable of representing every possible set of data. For instance, during a birthday party, users may want to share photos and videos of this event which can be seen as uploading streams of data to a content sharing system. This content stream will most likely have no index, unless it is explicitly generated, making its retrieval difficult. However, when clustering this stream, as data keeps increasing, we might, somewhere in the future, be capable of detecting similarities between each photo (e.g. a guest’s face) and might want to index them. Indices can directly impact a system’s performance however, there is a drawback from having either too many or too few indices, posing a challenge when it comes to evolving content. We propose Chives, a Content-Based Indexing framework, built on top of a content sharing publish/subscribe system at the edge named Thyme, where we evaluate unsupervised learning in data stream techniques to generate indices. It also offers a content-based query to automatically subscribe to indices containing similar content, e.g images. After evaluating our proposal in a simulated environment, we can see that our framework offers a great abstraction, allowing an easy extension, furthermore our implementation can generate indices from data streams and the indexing follows a clustering criteria, generating the indices as conditions are met. Furthermore, results show that our clustering quality and consequently its generated indices rely strongly on the quality of the image discrimination and its ability to extract features representing its face. In Conclusion, more studies should be done regarding this framework as such, our solution is built in a way where we can exclusively study each component and upgrade it in future work.Recentemente, tem-se observado um enorme crescimento na adesão a dispositivos móveis e com este crescimento, tem também aumentado a quantidade de dados partilhados, sendo em grande escala, gerado pelos utilizadores, por exemplo, fotos, livros, textos ou até mensagens/e-mails. Normalmente estes dados necessitam de um local de armazenamento permanente e a sua respectiva indexação de modo a poderem ser acedidos de forma eficiente por parte dos utilizadores no entanto, dada a imprevisibilidade destes dados, pode surgir um problema relativamente à indexação dado que poderá ser difícil prever etiquetas e índices capazes de representar qualquer conjunto de dados. Por exemplo, durante uma festa de anos, utilizadores poderão partilhar fotografias e vídeos deste evento que poderá ser também interpretado como um upload de dados em stream para um sistema de partilha de conteúdo. Esta stream de dados, muito provavelmente não terá nenhum índice capaz de o descrever, tornando difícil a obtenção deste visto que não existe representação semântica desta. No entanto, ao agrupar esta stream, à medida que os dados vão crescendo, poderemos, algures no tempo ser capaz de detectar semelhanças entre cada fotografia (por exemplo. a cara de um convidado) e podemos querer indexar. Índices podem causar um impacto directo sobre o sistema, no entanto o inverso pode acontecer quando existe índices em défice ou em excesso, apresentando um desafio acerca de dados evolutivos. Nós propomos uma framework de indexação baseada em conteúdo, construído por cima de um sistema de partilha de conteúdo que usa um sistema de Publish/Subscribe na edge denominado Thyme, onde avaliamos técnicas de aprendizagem não supervisionada em data streams para gerar dinamicamente índices. Depois de avaliar a nossa framework, conseguimos concluir que esta oferece uma boa abstração, facilitando a sua extensão, para além disso a nossa proposta permite gerar índices quando as condições definidas para o clustering são respeitadas. Para além disso, os resultados demonstram que o clustering realizado pelo nosso algoritmo dependem fortemente da qualidade de discriminação de imagens e das características obtidas por este discriminador em relação às faces. Concluindo, mais estudos devem feitos em relação à framework, como tal esta foi construída de modo a permitir uma rápida e fácil extensão para futuros melhoramentos