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Recently, the performance of neural image compression (NIC) has steadily improved thanks to the last line of study, reaching or outperforming state-of-the-art conventional codecs. Despite significant progress, current NIC methods still rely on ConvNet-based entropy coding, limited in modeling long-range dependencies due to their local connectivity and the increasing number of architectural biases and priors, resulting in complex underperforming models with high decoding latency. Motivated by the efficiency investigation of the Tranformer-based transform coding framework, namely SwinT-ChARM, we propose to enhance the latter, as first, with a more straightforward yet effective Tranformer-based channel-wise auto-regressive prior model, resulting in an absolute image compression transformer (ICT). Through the proposed ICT, we can capture both global and local contexts from the latent representations and better parameterize the distribution of the quantized latents. Further, we leverage a learnable scaling module with a sandwich ConvNeXt-based pre-/post-processor to accurately extract more compact latent codes while reconstructing higher-quality images. Extensive experimental results on benchmark datasets showed that the proposed framework significantly improves the trade-off between coding efficiency and decoder complexity over the versatile video coding (VVC) reference encoder (VTM-18.0) and the neural codec SwinT-ChARM. Moreover, we provide model scaling studies to verify the computational efficiency of our approach and conduct several objective and subjective analyses to bring to the fore the performance gap between the adaptive image compression transformer (AICT) and the neural codec SwinT-ChARM.

In our previous paper, we proposed a non-Gaussian Bayesian filter using power moments of the system state. A density surrogate parameterized as an analytic function is proposed to approximate the true system state, of which the distribution is only assumed Lebesgue integrable. To our knowledge, it is the first Bayesian filter where there is no prior constraints on the true density of the state and the state estimate has a continuous form of function. In this very preliminary version of paper, we propose a new type of statistics, which is called the generalized logarithmic moments. They are used to parameterize the state distribution together with the power moments. The map from the parameters of the proposed density surrogate to the power moments is proved to be a diffeomorphism, which allows to use gradient methods to treat the optimization problem determining the parameters. The simulation results reveal the advantage of using both moments for estimating mixtures of complicated types of functions.

A series of experiments in stationary and moving passenger rail cars were conducted to measure removal rates of particles in the size ranges of SARS-CoV-2 viral aerosols, and the air changes per hour provided by existing and modified air handling systems. Such methods for exposure assessments are customarily based on mechanistic models derived from physical laws of particle movement that are deterministic and do not account for measurement errors inherent in data collection. The resulting analysis compromises on reliably learning about mechanistic factors such as ventilation rates, aerosol generation rates and filtration efficiencies from field measurements. This manuscript develops a Bayesian state space modeling framework that synthesizes information from the mechanistic system as well as the field data. We derive a stochastic model from finite difference approximations of differential equations explaining particle concentrations. Our inferential framework trains the mechanistic system using the field measurements from the chamber experiments and delivers reliable estimates of the underlying physical process with fully model-based uncertainty quantification. Our application falls within the realm of Bayesian ``melding'' of mechanistic and statistical models and is of significant relevance to environmental hygienists and public health researchers working on assessing performance of aerosol removal rates for rail car fleets.

To integrate large systems of nonlinear differential equations in time, we consider a variant of nonlinear waveform relaxation (also known as dynamic iteration or Picard-Lindel\"of iteration), where at each iteration a linear inhomogeneous system of differential equations has to be solved. This is done by the exponential block Krylov subspace (EBK) method. Thus, we have an inner-outer iterative method, where iterative approximations are determined over a certain time interval, with no time stepping involved. This approach has recently been shown to be efficient as a time-parallel integrator within the PARAEXP framework. In this paper, convergence behavior of this method is assessed theoretically and practically. We examine efficiency of the method by testing it on nonlinear Burgers and Liouville-Bratu-Gelfand equations and comparing its performance with that of conventional time-stepping integrators.

We propose a dynamical low-rank algorithm for a gyrokinetic model that is used to describe strongly magnetized plasmas. The low-rank approximation is based on a decomposition into variables parallel and perpendicular to the magnetic field, as suggested by the physics of the underlying problem. We show that the resulting scheme exactly recovers the dispersion relation even with rank 1. We then perform a simulation of kinetic shear Alfv\'en waves and show that using the proposed dynamical low-rank algorithm a drastic reduction (multiple orders of magnitude) in both computational time and memory consumption can be achieved. We also compare the performance of robust first and second-order projector splitting, BUG (also called unconventional), and augmented BUG integrators as well as a FFT-based spectral and Lax--Wendroff discretization.

Knowledge graphs represent factual knowledge about the world as relationships between concepts and are critical for intelligent decision making in enterprise applications. New knowledge is inferred from the existing facts in the knowledge graphs by encoding the concepts and relations into low-dimensional feature vector representations. The most effective representations for this task, called Knowledge Graph Embeddings (KGE), are learned through neural network architectures. Due to their impressive predictive performance, they are increasingly used in high-impact domains like healthcare, finance and education. However, are the black-box KGE models adversarially robust for use in domains with high stakes? This thesis argues that state-of-the-art KGE models are vulnerable to data poisoning attacks, that is, their predictive performance can be degraded by systematically crafted perturbations to the training knowledge graph. To support this argument, two novel data poisoning attacks are proposed that craft input deletions or additions at training time to subvert the learned model's performance at inference time. These adversarial attacks target the task of predicting the missing facts in knowledge graphs using KGE models, and the evaluation shows that the simpler attacks are competitive with or outperform the computationally expensive ones. The thesis contributions not only highlight and provide an opportunity to fix the security vulnerabilities of KGE models, but also help to understand the black-box predictive behaviour of KGE models.

Graph Neural Networks (GNNs) draw their strength from explicitly modeling the topological information of structured data. However, existing GNNs suffer from limited capability in capturing the hierarchical graph representation which plays an important role in graph classification. In this paper, we innovatively propose hierarchical graph capsule network (HGCN) that can jointly learn node embeddings and extract graph hierarchies. Specifically, disentangled graph capsules are established by identifying heterogeneous factors underlying each node, such that their instantiation parameters represent different properties of the same entity. To learn the hierarchical representation, HGCN characterizes the part-whole relationship between lower-level capsules (part) and higher-level capsules (whole) by explicitly considering the structure information among the parts. Experimental studies demonstrate the effectiveness of HGCN and the contribution of each component.

Knowledge graph embedding, which aims to represent entities and relations as low dimensional vectors (or matrices, tensors, etc.), has been shown to be a powerful technique for predicting missing links in knowledge graphs. Existing knowledge graph embedding models mainly focus on modeling relation patterns such as symmetry/antisymmetry, inversion, and composition. However, many existing approaches fail to model semantic hierarchies, which are common in real-world applications. To address this challenge, we propose a novel knowledge graph embedding model---namely, Hierarchy-Aware Knowledge Graph Embedding (HAKE)---which maps entities into the polar coordinate system. HAKE is inspired by the fact that concentric circles in the polar coordinate system can naturally reflect the hierarchy. Specifically, the radial coordinate aims to model entities at different levels of the hierarchy, and entities with smaller radii are expected to be at higher levels; the angular coordinate aims to distinguish entities at the same level of the hierarchy, and these entities are expected to have roughly the same radii but different angles. Experiments demonstrate that HAKE can effectively model the semantic hierarchies in knowledge graphs, and significantly outperforms existing state-of-the-art methods on benchmark datasets for the link prediction task.

Multimodal sentiment analysis is a very actively growing field of research. A promising area of opportunity in this field is to improve the multimodal fusion mechanism. We present a novel feature fusion strategy that proceeds in a hierarchical fashion, first fusing the modalities two in two and only then fusing all three modalities. On multimodal sentiment analysis of individual utterances, our strategy outperforms conventional concatenation of features by 1%, which amounts to 5% reduction in error rate. On utterance-level multimodal sentiment analysis of multi-utterance video clips, for which current state-of-the-art techniques incorporate contextual information from other utterances of the same clip, our hierarchical fusion gives up to 2.4% (almost 10% error rate reduction) over currently used concatenation. The implementation of our method is publicly available in the form of open-source code.