Preasymptotic Convergence of Randomized Kaczmarz Method

Kaczmarz method is one popular iterative method for solving inverse problems, especially in computed tomography. Recently, it was established that a randomized version of the method enjoys an exponential convergence for well-posed problems, and the convergence rate is determined by a variant of the condition number. In this work, we analyze the preasymptotic convergence behavior of the randomized Kaczmarz method, and show that the low-frequency error (with respect to the right singular vectors) decays faster during first iterations than the high-frequency error. Under the assumption that the inverse solution is smooth (e.g., sourcewise representation), the result explains the fast empirical convergence behavior, thereby shedding new insights into the excellent performance of the randomized Kaczmarz method in practice. Further, we propose a simple strategy to stabilize the asymptotic convergence of the iteration by means of variance reduction. We provide extensive numerical experiments to confirm the analysis and to elucidate the behavior of the algorithms.Comment: 20 page

Integrated mode-locked lasers in a CMOS-compatible silicon photonic platform

CLEO: Science and Innovations 2015 San Jose, California United States 10–15 May 2015 ISBN: 978-1-55752-968-8 From the session: Silicon Photonic Systems (SM2I)The final version is available from the publisher via the DOI in this record.Integrated components necessary for a mode-locked laser are demonstrated on a platform that allows for monolithic integration with active silicon photonics and CMOS circuitry. CW lasing and Q-switched mode-locking are observed in the full structures.This work was supported under the DARPA E-PHI project, grant no. HR0011-12-2-0007

Development of Advanced Bioinformatics Tools for Integrating Genomic Data and Enhancing Diagnosis of Rare Diseases

Rare diseases pose significant challenges in diagnosis and treatment due to their genetic complexity and the limited availability of comprehensive genomic data. Current bioinformatics tools often struggle with accurately detecting rare mutations and integrating diverse genomic and clinical data, leading to delays in diagnosis and suboptimal patient care. This research proposes the development of an advanced bioinformatics pipeline aimed at enhancing the accuracy of mutation detection, integrating genomic, phenotypic, and clinical data, and providing a user-friendly interface for clinicians. The pipeline uses machine learning algorithms for improved mutation calling and data integration techniques to correlate genetic variants with clinical outcomes. The tool was evaluated on multiple rare disease datasets, demonstrating significant improvements in diagnostic accuracy and efficiency. With precision and recall rates of 92% and 88%, respectively, and a 40% reduction in diagnostic time, this approach promises to revolutionize rare disease diagnostics by facilitating faster, more accurate diagnoses and personalized treatment options

2022 Roadmap on integrated quantum photonics

AbstractIntegrated photonics will play a key role in quantum systems as they grow from few-qubit prototypes to tens of thousands of qubits. The underlying optical quantum technologies can only be realized through the integration of these components onto quantum photonic integrated circuits (QPICs) with accompanying electronics. In the last decade, remarkable advances in quantum photonic integration have enabled table-top experiments to be scaled down to prototype chips with improvements in efficiency, robustness, and key performance metrics. These advances have enabled integrated quantum photonic technologies combining up to 650 optical and electrical components onto a single chip that are capable of programmable quantum information processing, chip-to-chip networking, hybrid quantum system integration, and high-speed communications. In this roadmap article, we highlight the status, current and future challenges, and emerging technologies in several key research areas in integrated quantum photonics, including photonic platforms, quantum and classical light sources, quantum frequency conversion, integrated detectors, and applications in computing, communications, and sensing. With advances in materials, photonic design architectures, fabrication and integration processes, packaging, and testing and benchmarking, in the next decade we can expect a transition from single- and few-function prototypes to large-scale integration of multi-functional and reconfigurable devices that will have a transformative impact on quantum information science and engineering