Perturbation-Assisted Sample Synthesis: A Novel Approach for Uncertainty Quantification

This paper introduces a novel generator called Perturbation-Assisted Sample Synthesis (PASS), designed for drawing reliable conclusions from complex data, especially when using advanced modeling techniques like deep neural networks. PASS utilizes perturbation to generate synthetic data that closely mirrors the distribution of raw data, encompassing numerical and unstructured data types such as gene expression, images, and text. By estimating the data-generating distribution and leveraging large pre-trained generative models, PASS enhances estimation accuracy, providing an estimated distribution of any statistic through Monte Carlo experiments. Building on PASS, we propose a generative inference framework called Perturbation-Assisted Inference (PAI), which offers a statistical guarantee of validity. In pivotal inference, PAI enables accurate conclusions without knowing a pivotal's distribution as in simulations, even with limited data. In non-pivotal situations, we train PASS using an independent holdout sample, resulting in credible conclusions. To showcase PAI's capability in tackling complex problems, we highlight its applications in three domains: image synthesis inference, sentiment word inference, and multimodal inference via stable diffusion

Momentum-space entanglement after a quench in one-dimensional disordered fermionic systems

We numerically investigate the momentum-space entanglement entropy and entanglement spectrum of the random-dimer model and its generalizations, which circumvent Anderson localization, after a quench in the Hamiltonian parameters. The type of dynamics that occurs depends on whether or not the Fermi level of the initial state is near the energy of the delocalized states present in these models. If the Fermi level of the initial state is near the energy of the delocalized states, we observe an interesting slow logarithmic-like growth of the momentum-space entanglement entropy followed by an eventual saturation. Otherwise, the momentum-space entanglement entropy is found to rapidly saturate. We also find that the momentum-space entanglement spectrum reveals the presence of delocalized states in these models for long times after the quench and the many-body entanglement gap decays logarithmically in time when the Fermi level is near the energy of the delocalized states.Comment: 4+e pages, 3 figure

An Overview of Human Activity Recognition Using Wearable Sensors: Healthcare and Artificial Intelligence

With the rapid development of the internet of things (IoT) and artificial intelligence (AI) technologies, human activity recognition (HAR) has been applied in a variety of domains such as security and surveillance, human-robot interaction, and entertainment. Even though a number of surveys and review papers have been published, there is a lack of HAR overview papers focusing on healthcare applications that use wearable sensors. Therefore, we fill in the gap by presenting this overview paper. In particular, we present our projects to illustrate the system design of HAR applications for healthcare. Our projects include early mobility identification of human activities for intensive care unit (ICU) patients and gait analysis of Duchenne muscular dystrophy (DMD) patients. We cover essential components of designing HAR systems including sensor factors (e.g., type, number, and placement location), AI model selection (e.g., classical machine learning models versus deep learning models), and feature engineering. In addition, we highlight the challenges of such healthcare-oriented HAR systems and propose several research opportunities for both the medical and the computer science community

Discrete gravitational approaches to cosmology

Exact solutions to the Einstein field equations are notoriously difficult to find. Most known solutions describe systems with unrealistically high degrees of symmetry. A notable example is the FLRW metric underlying modern cosmology: the universe is assumed to be perfectly homogeneous and isotropic, but in the late universe, this is only true on average and only at large scales. Where an exact solution is not available, discrete gravitational approaches can approximate the system instead. This thesis investigates several cosmological systems using two distinct discrete approaches. Closed, flat, and open ‘lattice universes’ are first considered where matter is distributed as a regular lattice of identical point masses in constant-time hypersurfaces. Lindquist and Wheeler’s Schwarzschild–cell method is applied where the lattice cell around each mass is approximated by a perfectly spherical cell with Schwarzschild space–time inside. The resulting dynamics and cosmological redshifts closely resemble those of the dust-filled FLRW universes, but with certain differences in redshift behaviour attributable to the lattice universe’s lumpiness. The application of Regge calculus to cosmology is considered next. We focus exclusively on the closed models developed by Collins, Williams, and Brewin. Their approach is first applied to a universe where an exact solution is already well-established, the vacuum Λ-FLRW model. The resulting models are found to closely reproduce the dynamics of the continuum model being approximated, though certain constraints on the applicability of the approach are also uncovered. Then using this knowledge, we next model the closed lattice universe. The resulting evolution closely resembles that of the closed dust-filled FLRW universe. Constraints on the placement of the masses in the Regge skeleton are also uncovered. Finally, a ‘lattice universe’ with one perturbed mass is modelled. The evolution is still stable and similar to that of the unperturbed model. The thesis concludes by discussing possible extensions of our work.The numerical simulations of the Lindquist–Wheeler models in Chapter 2 were performed on the COSMOS Shared Memory system at DAMTP, University of Cambridge, operated on behalf of the STFC DiRAC HPC Facility. This equipment is funded by BIS National E-infrastructure capital grant ST/J005673/1 and STFC grants ST/H008586/1, ST/K00333X/1, and ST/J001341/1. The PhD was financed in part by a bursary from the Cambridge Commonwealth Trust. Additionally, the author was twice granted generous Rouse Ball Travelling Studentships by Trinity College, Cambridge, as well as commensurate travel funds by DAMTP to attend academic conferences in Beijing, China, and Jena, Germany